The hypermodern openings. For White that would be the English Opening (1. c4), Zukertort Opening (1. Nf3), and the fianchetto openings (1. b3, 1. g3), and for Black that would be the fianchetto defenses or other hypermodern openings (Pirc Defense, Alekhine's Defense, etc.).
Another idea is to play systems: Colle System, Hippopotamus, London System, etc.
French defense. That is what attracted me to the French defense at the start, because it is more about understanding the plans and structure instead of memorize a lot of line (Winawer variation is kind of an exception, but you can bypass that as black by playing the classical variation)
With White, the d4 system openings: Colle, Zukertort, London etc. With Black the Black Lion.
I find the Paulsen (e6) Sicilian to be extremely untheoretical, simply because both sides have many choices and few of them are critical or "one move only". In my opinion, playing such an opening, which can lead to sharp positions, is more difficult than playing lines that can be memorised because they're heavily analysed or have relatively few viable divergencies.
Both sides of the Ruy Lopez. There’s theory, but very little of it is critical, and typical plans and ideas abound throughout the whole game
Veresov's Opening, where you (White) play 1 d4 2 Nc3 3 Bg5 almost no matter what Black plays is one.
The Caro-Kann and Slav Defenses both play 1...c6 (can be played against 1...e4 1...d4 1...c4, etc.) 2 d5, move the QB to f5 or g4 so it won't get trapped behind it's own Pawn Chain before playing ...e6, play the QN to Q2, and you've got a solid base to absorb White's initial attack, then you can respond with either ...c5 (preferred), ...b6, or ...f6 depending on how the game develops, usually attacking on the Q-side.
These defenses allow you a lot of leeway because they are solid defenses but your pieces are not tripping over each other because you got your Bad Bishop outside the Pawn Chain.
For 1 e4 e5, as White I've liked the Bishop's Opening because it involves 1 e4 2 Bc4 3 d3 4 Nc3 and often 5 f4 - starting a K-side attack before putting your KN on f3. If Black castles K-side, you castle Q-side, storm your h, g, and f Pawns at Black's castle and relentlessly aim every piece you can at your opponent's king.
For 1 e4 e6, the Advance Variation requires little book knowledge as long as you know you have to protect your Q-side from the attack Black will begin with ...c5.
For 1 e5 c5, the c3 (Alapin) Sicilian results in good positions where you are not giving up your center d-Pawn for Black's c-Pawn.
In each case, you don't have to memorize reams of opening data because you understand the ideas behind the openings and, if you play them often enough, you know what works with them!
The London System (1 d4 2 Nf3 3 Bf4) similarly bulid
What do you think are the best openings for white and black to play with ideas and plans and not memorization of lines?