Most of the GM games I've seen have started with one of those two. I think the difficulty comes when you learn openings and variations based on them.
What's the most strategic way to start a game (if you're playing white)?

I think the Queen’s gambit is very good; it’s not really a gambit since it’s easy to gain back the lost pawn! And plus, two center pawns are always great to have.
The choice of opening depends on what you are comfortable playing, are there openings you want to avoid and if you know your opponent, either trying to exploit their weaknesses or avoid their strongest openings. The opening move is not crucial in this. The four most popular ones are e4, d4, Nf3 and c4. But even if you start 1. e4 e5 it does not define the nature of the opening - you can continue with 2. Nf3 (most popular), 2. Nc3 (more passive), 2. f4 (more aggressive) or 2. d4, each leading to a different type of play (but capable of transposing). There are about 20 reasonable openings with hundreds of reasonable variations based on 1. e4 or 1. d4, so choosing either of them does not mean that you will be predictable.
If you decide to play one of the more rare openings (say 1. b3, 1. g3 or 1. b4), the response will be that Black takes over the center and you need to play accurately or you will find yourself in trouble, though at a beginner level middle game will be decisive. But once you go beyond beginner level (=when hanging pieces becomes rare), a passively played flank opening will nearly always lead to a bad position and losing the game. I have seen a couple of players specializing in one of the rare openings and being familiar with it, they are able to play well against better opponents despite giving up the center control.

Don't play complex openings. e4 and d4 are good. If you like open games, play e4 and keep it open. If you like closed, positional games d4 is good for you, but don't go beyond these because other openings are pretty complex, save that for when you are very high rated.

If you decide to play one of the more rare openings (say 1. b3, 1. g3 or 1. b4), the response will be that Black takes over the center and you need to play accurately or you will find yourself in trouble, though at a beginner level middle game will be decisive. But once you go beyond beginner level (=when hanging pieces becomes rare), a passively played flank opening will nearly always lead to a bad position and losing the game. I have seen a couple of players specializing in one of the rare openings and being familiar with it, they are able to play well against better opponents despite giving up the center control.
Hypermodern principle: control the center, but not necessarily occupy it. I've played hypermodern since I was 1100 because I'm a sadistic person :)

I usually start with the King or Queen's Pawn Opening, but I'm not sure what the best way is. I'm pretty sure it's the most popular opening, and I don't want to be that predictable, so...
Maybe Queen's pawn opening. Not necessarily Queen's Gambit, as it can get pretty boring sometimes. Maybe Colle System. English would be a good strategic opening, but requires quite a bit of study of hypermodern principles.
All this talk about hypermodern ideas and whatnot is most inappropriate. The opening poster just needs to learn opening principes. A good source for example:
However, it is even more important to take pieces that are hanging and not hang your own. Take this game, for example, it is really shocking:
https://www.chess.com/live/game/5819677162
The first thing to do is to stop hanging pieces. This is so important that nothing else really matters.
I usually start with the King or Queen's Pawn Opening, but I'm not sure what the best way is. I'm pretty sure it's the most popular opening, and I don't want to be that predictable, so...