Best way for white to refute the HyperAccelerated Dragon?

. e4 c5 2. Nf3 g6 

so the 3 best choices seem to be

d4, c3, c4

I usually play d4.... then recapture with the knight, but some people recapture with the queen forcing nf6... is this good for white?

It's a line like any other. You aren't going to refute a mainline opening.

c3 is playable, but avoid the line 1.e4 c5 2.Nf3 g6 3.c3 Bg7 4.d4 cxd4 5.cxd4 d5 6.e5 (6.exd5!?) Nc6 7.Nc3?! Bg4! (7.h3 was better I think)

c4 leads to a type of Maroczy bind usually.

d4 leads to mainline Accelerated Dragon positions usually, unless White tries the independent 4.Qxd4. White tends to score well in this line but I think both players need to know their stuff. One critical line runs 4...Nf6 5.e5 Nc6 6.Qa4 Nd5 7.Qe4 Ndb4 8.Bb5 Qa5 9.Nc3 Bg7 10.O-O where I think White has good chances to maintain an advantage.

I am so glad I do not have to worry about this problem as a result of the move order I play it from.

1.Nf3 g6 2.d4 Bg7 3.e4 c5 4.dxc5! Qa5 5.c3 Qxc5 6.Na3, and this position is one black should avoid, he is going to be down some 2 or 3 tempos compared to a normal looking sicilian. 

You may run into this move order occasionally though.

It is fun to know why 6..Bxc3+ is outright refuted.

I don't believe there is a refutation for the Hyper-Acclerated Dragon,  Did you look this up in the Game Explorer? It sounds (well reads actually) like you did at least up to move 3.

I think doing so past move 3 for several more moves would be helpful  -just check out the most popular choices not every single move ever played. Next why not just start playing 4.Qd4 and see if it works for you or not? What matters here isn't "is it good for White" since it appears to be sound but "is it good for YOU?"

Playing a few online games with openings you want to experiment with would also be a good idea if you have the patience, that way you can look through the Game Explorer and/or books and/or other DBs (www.365chess.com has a bigger opening DB than the Game Explorer you can also refer to)

One doesn't have to play well, it's enough to play better than your opponent. TARRASCH

Chesslive.de is the best free database available, lots and lots of stuff there.

Why is it that weak players always talk about refutations?

So that they don't have to think during the game.

Agreed, 7...Nbd4 is a little trappy in my opinion, hoping for 8.a3 d5! whereupon White retreats the queen, since 9.exd6 e.p. is met by Bf5.

Maroczy bind is probably considered White's best try for an advantage, although I consider it much more comfortable for Black than most people do.