For White, what should I play against the Sicilian that is positional, strategic, quiet, slow?

There's the Open Sicilian with Be2 and O-O. What would I play against the Classical Sicilian? Against the Classical Sicilian, 6.Be2 and O-O is barely playable but objectively not very strong, 6.Bg5 the Richter-Rauzer is sharp, tactical and theory-heavy.

There's 3.Bb5. Against 2...d6 it's called the Moscow. Against 2...Nc6 it's called the Rossolimo. But what would I play against 2...e6, 2...a6 and 2...g6? I can't play 3.Bb5 against these three moves.

There's 2.Nc3 3.g3. It's objectively not very strong. It feels strange to play g3 when I have already played e4, since these two moves have the same goal: to develop the King's Bishop. Why spend two moves to accomplish this goal when it can be accomplished in just one move?

What about the Alapin? Is it positional, strategic, quiet, slow, theory-light?

This is why I quit e4 and kinda gave up on claiming advantages in openings period. Against some Sicilians you can play a quiet positional game and claim an advantage, but against many the only path to a real advantage is in a theoretical blood bath. Assuming you want to play e4 and don't want to learn 40 million moves of opposite castling theory, I would say your best bets are either the closed or Alapin and being fine with even positions.

It's much easier to play slow and quiet at the start after 1. d4, 1. c4, or 1. Nf3 than 1.e4, so the first move is already an issue.

1. e4 c5 2. Nf3 e6 3. b3, 2. Nf3 a6 3. g3 (or 3. c3), 2. Nf3 g6 3. c3 would be principled ways to use the drawbacks of Black's second move.

6. h3 is popular against the Najdorf; maybe it can be played against the classical as well ?

@1

"There's the Open Sicilian with Be2 and O-O." ++ Yes.

"Against the Classical Sicilian, 6.Be2 and O-O is barely playable" ++ It is fine.

"There's 3.Bb5. Against 2...d6 it's called the Moscow. Against 2...Nc6 it's called the Rossolimo."
++ Yes

"what would I play against 2...e6, 2...a6 and 2...g6?" ++ E.g. 3 d3.

"There's 2.Nc3 3.g3. It's objectively not very strong." ++ Smyslov and Spassky played it.

"It feels strange to play g3 when I have already played e4" ++ For firm control over d5.

"Why spend two moves to accomplish this goal when it can be accomplished in just one move?"
++ Because at g2 it controls 2 central squares: e4 and d5.

"What about the Alapin? Is it positional, strategic, quiet, slow, theory-light?"
++ Yes. Sveshnikov recommended it.

if you dont mind the queenside space disadvantage, closed sicilian is not a bad choice, i know it has a reputation for being agressive but in truth, the best ways to counter the kingside are well known, so often it turns into an asymmetrical positional struggle,

the bb5+ lines delay the tension of d4 and can be played positionally.

personally i like g3 open sicilians agaisnt most sicilian variations. They usually dont give you as much of a first move advantage as more agressive main lines, but they are very prophylactic and you can pretty often remove all of black's counterplay and have a small advantage to boot.

Superficial.

First, that sort of formation (combining e4 with g3 and Bg2) is strong enough that both Spassky and Fischer played it repeatedly. Carlsen has played it against Anand, Giri, Nepomniatchchi and MVL.

Second, developing the f1-Bishop is only one of the ideas behind 1. e4. Restraining Black from playing d7-d5 is another important motive for that move... and this restraint is tripled if you get in e4 and Nc3 and Bg2. All three moves bear down on the d5 square.

I would also like to add that OP wanted something that was "quiet" and "slow" against the sicilian, an opening that begins with a pawn move that allows you to develop zero pieces. Of course something that's slow and quiet is not going to be as theoretically challenging.

for me? 2. c4 or b4 are my current thoughts.

What do you prefer? That should help your choice(s) on how to play.

@8
2 b4 is a dubious gambit and 2 c4 leaves a hole on d4. Neither is a development move.
Better 2 Nf3, 2 Nc3, 2 c3, 2 Bc4, 2 f4.

The Rossolimo is excellent. The alapin is great against 2... e6, better than in other contexts. Against 2...d6 setup I prefer the princ variation over the Moscow... 1. e4 c5 2. Nf3 e6 3. d4 cxd4 4. Nxd4 Nf6 5. f3. I don't really see the need to play the Moscow if you're playing the Rossollimo, they're not going to transpose very often and your repertoire is already very compact playing all these anti-sicilians.

A good way to learn the sicilian is to start off with an anti-sicilian repertoire with white like this, and then play as black more mainline sicilians... and gradually start playing both sides of it. Though nowdays the Rossollimo is actually starting to be considered the main line. But maybe as black start with the french sicilians

Poison Pawn variation of the Najdorf. Sorry couldn't resist

At the super-GM level (2700+), since 2020, after 1.e4 c5 2.Nf3 Nc6, 3.Bb5 has been played 2.8 times more frequently than 3.d4.

well super gm level is like 30 people, the fashion choice of 4-5 players can tilt that greatly

At the GM level (2500+) (that's like 1000 people), 3.Bb5 has been played 1.9 times more frequently than 3.d4.

Hi,

I think that both the Closed Sicilian and the Rossellini variation are positional ways to play. 
However, they lead to very different types of games. 
The Closed Sicilian keeps pieces on the board and so leads to a more complex maneuvering game. The Rossolimo can lead to early exchanges and a simplified pawn structure. 

both are “ positional” ways to play but they differ in complexity or tension.

my two cents.