I think just starting out the english. or if you prefer e4 then the scotch or open sicilian. for black caro-kann for e4 and e6 d5 structures for d4.
Best first opening repertoire for beginners to improve

I would say
1.e4
- Italian ( Evans and Two Knight Scotch ). Scotch also very good.
- 3.Nc3 vs French. Tarrasch also acceptable. Advance variation or Milner berry gambit also good options.
- Take on d5 and just develop naturally against the scandi.
- 150 Attack against the Pirc is king. 👑
- Alapin Sicilian is a good anti Sicilian, the Magnus/Tiviakov Sicilian combo is also great 👍. Smith Mirra cannot be forgotten. And the Open Sicilian is awesome. Main recommendations are Open Sicilian or Alapin though.
- Two Knights Caro is very good. Advance Caro is very good. Panov is very good. Fantasy is fine. Main recommendation is Advance Caro ( Tal and short variation are both fine. )

Black -
- E5 vs e4. Honestly doesn’t matter which variation you pick against different things. Against scotch, Bc5 and Nf6 are both fine. Against Italian, both Bc5 and Nf6 are fine as well. Against Ruy, a6 is fine, Nf6 is fine, f5 is also fine.
Sicilian is also a good option. But I’d recommend the classical or the accelerated dragon. Possibly a Kan or o Kelly. All of them being good “starter” Sicilians imo
I also don’t have a problem with caro Kann or French.

If you hold a hot take like “adopting a system (KIA, Colle, etc.) is a bad idea because it would sacrifice the long term improvement for the short term“ to be axiomatic,
then why bother asking us for advice in the first place?
I read multiple times that adopting a system sacrifices the long term for the short term improvement because it makes beginners play robotically on auto-pilot without taking into account what their opponent does so it doesn't teach them the general opening principles. So I thought it was an uncontroversial fact, but perhaps I was wrong. Please do share your line of reasoning if you disagree.
Playing for a variety of systems may be a solution. Like playing d4 nf3 and choosing between colle, london or torre. The torre option is the most interesting. You can transpose it into a stonewall without the locked bishop. Thats how one can play 4 different systems switching between them every game.

Hi! Here my suggestion for beginners:
White: 1.e4
Black: Meet 1. e4 with 1...e5 and 1. d4 with...1.d5
Meet any other first move either with 1...d5 or 1...e6 followed by 2...d5
For more details check my post on my blog: https://www.chess.com/blog/maafernan/openings-for-beginners
Good luck!

i would recommend playing open games like the ruy lopez as white
and as black i would recommend learning the plans for black agianst the italian/scotch/ruy lopez
also learn how to refute dubious openings like the wayward queen attack or the poziani
if you ever see a weird looking opening that you have never seen before i recommend searching it up and looking for ways to go agianst it

I agree with many suggestions here and would recommend for White to build around the Italian, starting with 1. e4 e5 2. Nf3 Nc6 3. Bc4 ... and then concentrating on one line for Black's response of either 3. ... Bc5 or 3. ... Nf6.
As the player improves, they can expand on that to include Scotch Gambit, Evan's Gambit, Bird's Attack (1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. b4 ..., which isn't common, but is sound), Moeller Attack 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 exd4 6. cxd4 Bb4+ 7. Nc3
Nxe4 8. O-O Bxc3 9. d5 {This defines the Moeller Attack Line } 9. ... Ne5 10. bxc3 Nxc4 11. Qd4 ... and so forth. There are lots of openings that sort of revolve around White's set up with the B on c4, focusing on Black's weak pawn on f7. Some are quieter and more positional, others are wild attacking games, and until someone gets to 2000+, they need to work on all aspects of the game and develop an understanding for both types of positions.
And, if they are learning the above, then they should also be learning it from both White and Black's perspective, hence 1. e4 e5 is a good starting point. Nothing wrong with Petroff's being added if they want to diverge as Black. It often requires slower positional play after an initial wave of exchanges as once the dust settles the positions are often very symmetrical. But again, that can be viewed as a good teaching opportunity. Against 1. d4, then again, QGD is a solid choice. They can add other options later.
If as White they are facing something other than 1. ... e5 often, then find one line for them to focus on against that (be it the French, Caro, Sicilian - for the latter maybe the Grand Prix attack as it is good at lower levels and probably up to around 2000 and helps keep them getting distracted by the huge amount of theory required to deal with all the possible choices Black can make).
But the focus at beginner level should be on end game skills. Master Q+K and R+K vs lone K checkmating (simple, but I've seen a lot of players take forever to work it OTB). Master K+P vs King end games, so they can recognize when it is a win (and how to do it every time), and when it is a draw (and how to make it so if they're the lone King!). After that, learn 2B+K and B+N+K vs lone King mating patterns. Not common in practice, but results in good piece coordination understanding. Focus on recognizing the basic checkmate patterns. Basically, end game skills are far more important than opening theory - as the game progresses the player moves more and more towards their strength rather than away from it.
Also, knowing where one is trying to get to is a really big asset when evaluating middle game tactics and choices. So after end game skills the next major focus should be on middle game tactics and positional understanding.
Too much time spent on studying the opening phase means too little time on the bulk of the game, and in the end, lower level opponents are not going to know the theory all that well either, so it's a lot of time memorizing moves that they will never get to play, and don't understand either.

There's another approach which may be helpful to your students.
I like this book by Bruce Alberston: "51 Chess Openings for Beginners." He explains just the first five moves (10 ply) for each opening. After that, they are on their own.
Instead of narrowly specialising at a young age, your students can play out games using this wide variety of openings.
This approach emphasises adaptability, flexibility, ingenuity and versatility over narrow specialisation. It emphasises over-the-board skills (Lasker-style) instead of rote memorisation of long lines of theory. It's great for learners because it exposes them to a wide range of chess positions. They learn opening principles by practical play.
Of course, if they are ambitious as players, they can specialise later. But at the stage you are talking about, it's a good way of learning about many openings.
For example, you can choose a few openings each week and instruct the class to play with just those openings. It's easy for the kids to learn the moves by heart, because there are only a few of them. But they also understand the reasons for those moves.
At the end of the week, you have a review session or two to discuss what the students found out (by their practice, not by theory) about each type of opening. You pick out a few games they played and review them together. That way, they get feedback on what they did and what they could have done.
Then the next week, you choose a different set of openings and practise those. And so on. I myself have taught classes of kids with this book, and it works out very well.

Another thing I do is to make a jpeg of each board position at the end of each 10-ply opening in that book. I send them round in random order to the kids and ask them which opening it is (a recognition test of what they have already learned). Then: can they reconstruct the moves which led to these positions?
I want them to be able to recognise a wide variety of openings and the typical positions they lead to, and these "end-backwards" puzzles are good for making them think about that in a different way.
Example: what are these openings? What moves led up to them?
Answers: Bird's Opening, Bogo-Indian Defence, Centre Game, Colle System.

Another thing I want the kids to learn - by heart - is the key move for each opening, the one that defines it. It's the anchor for that opening.
This is valuable in two ways: 1. When they want to play that opening. 2. For recognising what opening their opponent is playing against them.
For example, the key move for the Bogo-Indian Defence is 3 ... Bb4+. I teach this first, and then test it.
Test 1: I call out the move (3 ... Bb4+) and they tell me the opening.
Test 2: I show them the board position just before the key move, and tell them they are going to play the Bogo-Indian. So what's the next move?
Test 3: I show them the board position just after the key move 3... Bb4+ has been played, and they have to tell me what the opening is.
Test 2 is "I give you the opening name, you tell me the key move".
Tests 1 and 3 are "I give you the key move, you tell me the opening".
All of these ways are to help imprint the opening patterns in the kids' minds and to get them to think creatively about how they are arrived at.
Tricky transpositions are taught a bit later, because that is more advanced stuff. But the principles are the same.
An easy repertoire is this:
White: London System with Torre against g6 variations and an anti Benoni against c5 variations.
Black: French with 1.e4 e6 ( Fort Knox in the beginning) and 1.d4 e6 (if 2.c4 Bb4+) and 1.c4 e6...
Many patterns repeat and easy to start with.

Bump.
You write bump, but how about responding to the posts already made? I put three here.

@Lotus960: I'm asking for the best openings for beginners, so I'm not really interested in your idea of telling a beginner to play every single openings in existence, changing to a completely different opening repertoire every week.

White: London system, queens gambit, stonewall, e4 Nf3(scotch/italian/4 knights/ponziani and NO RUY LOPEZ), Vienna game with g3 or bc4, Wayward queen attack, bishop's opening with 2.d3. Reti with no theory only opening prinziples.
Black: Scandivavian with Qa5, Scandinavian modern(Portugiese and icelandic gambits) for more agressive play. Sicilian(hyperaccelerated dragon, kalashnikov, french) e4 e5, Nimzowitsch with 2.d5(yes), Lion's defence, Englund gambit, d4 d5, old benoni.
both: king's indian setup.
Thats literally it
My experience is that I didnt improve by studying openings. I improved through learning openings by studying full games of a good player.
I'd suggest: pick a GM with a book he /she annotated themselves of their games, study the full games and mimic their opening choices. For specifics, I know lots of strong players who got there by studying Keres' games intensely. Also Capablanca, also Fischer, also Botvinnik and Smyslov and Morphy.
I wore out my book of Keres' games long ago. Lately I've been working thru the little Dover book of Euwe's games. His play is very clear, active and direct so could be a good choice too.
So my suggestion is learn openings by studying full games of a player whose play you want to learn from.
my opinion only, Bill
As for my opening choices.
Opening for beginners should be choosen on the factors whether an opening follows general opening principles or not. If it does it is fine.
Basic opening principles:-
Put pawns in the centre.
Prioritize Development.
Castle quickly
Don't bring queen out too early.
Don't move same piece twice.
Have a middlegame plan in mind. Don't mindlessly follow opening principles.
The last principal is the one which will put a tight slap on delusional people who tell not to learn openings unless someone is 2000 FIDE.
When we learn opening they don't learn moves but also get the ideas on what potentially to do in a middlegame. Why a certain move is played? that gives better understanding of chess as a whole.