The idea of a pawn storm is to exchange pawns and open files; so the 'usual' defence against a pawn storm is to keep the files closed, which often entails responding to an offer to swap pawns by advancing your own, e.g. if white plays h6, black will want to play ...g6.
So from the attacker's viewpoint, you will want to make use of the weaknesses created by any change in your attacker's pawn structure, or force a pawn exchange. In the position you have given, your pieces are not too well placed; only your knight plays a role in the attack on the king, and the queen is ready. The bishop on f4 is a liability in lines where the f-file is opened, and you would much rather have a rook on g1.
Personally, I would prefer to start with Rg1 because in almost all cases, you will need to put a rook on the g-file.
In fact, after this move you are threatening 2. Qd4, forcing 2 ...f6 where black's position collapses after 3. Nxg7. You are threatening 2. h5 and 3. g6, after which your position will be crushing, because of the piece sacrifices you have available.
You usual concern as the attacker (especially when material is equal) is the counterattack of the opponent, as the success of your attack is only a matter of time. In the case of this position, black's a4-a3 advance is too slow (you can even ignore it and allow ...axb2 and your position is not immediately busted yet), so you can even ave the luxury of making another prepatory move like Be3.
For any attack against the king, the attacker generally wants to force the advance of the pawns covering the king, so pawns on f7-g7-h7 are usually the most resistant to an attack. Often he does this by tempting the move ...h6 by placing a piece on g5. This position looks much like the Petroff after 1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nf3 Nxe4 5. Nc3 Nxc3 6. dxc3, and is probably what you played if I had to guess. I recall Morozevich winning a game in this line as white, which you could probably look up.