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.
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