It all depends. Again one necessarily has to think game-theoretically. For example putting in big bets allows you to bluff more often while being close to an unexploitable strategy. If on the other hand you want to exploit your opponent because, say, you think he folds too often, you would want to put in the smallest size possible that still makes him fold at a high rate. Putting in big sizes in that situation will decrease your EV, possibly to the point where it's no longer a profitable strategy.
Asking about the "bet size" in any specific no-limit situation is very much like asking this:
"...which direction should I move my pawn?"
It's very difficult to answer. It's almost impossible to give an answer. Because there is no answer.
I mean, there are sometimes only a couple obvious moves, fold or raise. And raises often go:
2x, 3x, 4x.... all-in
Meaning, after you 3 or 4x someone's bet, a 5x is pretty much all in.
There's a handful of moves.
Often it's like playing rock/paper/scissor.
You may think, "oh, well, that's simple now."
The simpler it is, the easier it is to exploit a known advantage.
The simpler it is, the more players can play, because, like checkers, it's easier to pick up.
So, more players equals more overall dead/easy money.
Now back to the bet size.
The bet size is a series of maneuvers in a very long game of fencing/chess/soccer.
Whatever, you could work the entire game to set your opponent up for one fell death blow.
Often, like boxing, you're just trading jabs, waiting for the kill shot, waiting for the opponent to leave his jugular a bit unguarded.
So I'll never have an answer to a very general question like "what is the right bet size for such and such situation?"
The reason is because you made up a fake situation.
And sure I could make up some generalities that state: "most of the time you should do this..."
And following that advice could make you a winning player.
But really, the ultimate goal of doing something, for me at least, when it comes to something that is competitive, that goal is to win. Otherwise, why compete?
Why not just put it on casual mode if you're not going to put up a fight?