You're not being naive.
It sounds like you're a positional player. You'll probably favor closed games. Closed games are ones where there are pawns in the center, reducing the long-range power of many of the pieces on the board.
Too much memorization is unhelpful. You will need to memorize a a few openings, and not too deeply. As long as you understand what the openings are trying to accomplish and you know basic principles you'll be fine.
For openings, play
1. d4, and work through some main lines of the Queen's Gambit. From this link, you'll see that your play won't change much for the first few moves; there's a theme.
If you're on the black side of the board, you have more choices. You'll probably see
1. e4 more than
1. d4. For the latter, look at the 'closed game' and similar:
1. d4 d5
2. c4 e6
3. Nc3 Nf6
4. Bg5 Be7
5. e3 O-O
6. Nf3 Nbd7
See how black avoids lines where the center pawns get traded off?
1. e4 you'll be looking for the same thing - lines that leave the pawns on the board or at least, like this Caro-Kann, leave a solid position:
1. e4 c6
2. d4 d5
3. Nc3 dxe4
4. Nxe4 Bf5
5. Ng3 Bg6
6. h4 h6
7. Nf3 Nd7
8. h5 Bh7
9. Bd3 Bxd3
Here's a link for a plethora of e4 openings.
Which opening to pick? Narrow down the field by examining games of Anatoly Karpov, Tigran Petrosian, Aron Nimzovitch, and Mikhail Botvinnik. Nimzovitch is the godfather of the 'prophylactic' style you describe. You might get a copy of 'My System', one of the first books to collect, state, and explain the principles of positional play. Be advised this book (and many others) are old and were written using the now-obsolete 'descriptive' notation. You probably want your copies to be in algebraic or figurine algebraic notation. If you buy a copy off of e-bay etc you should verify what you're getting.