There is a lot of good advice so far. Here is my own contribution.
I have generally played the Grand Prix after 1.e4 c5 2.Nc3 Nc6 3.f4 and 2...d6 3.f4 (though 3.d4!? is also quite interesting here, with transposition to the Chekhover as demonstrated in some Gad Guseinov games). However, I find that the Closed lines simply give White no advantage against 2...e6! and so I also recommend switching to the Open with 3.Nf3 Nc6 4.d4 etc. I generally angle toward the fianchetto lines (as discussed in Nigel Davies's Taming the Sicilian -- and see more below), but lines with d4 followed eventually by f4 are also interesting for the Grand Prix player (as discussed in Dangerous Weapons: The Sicilian, for instance).
I often have opponents play 1.e4 c5 2.Nc3 e6 3.Nf3 d5?! (which can also arise via the Two Knights French), but White seems to get a big advantage, as shown in a Dana Mackenzie video at ChessLectures.com:
[Event "?"]
[Site "?"]
[Date "2007.??.??"]
[Round "?"]
[White "Popov, Mikhail"]
[Black "Savchenko, Alexei"]
[Result "1-0"]
[ECO "C00"]
[TimeControl "240+2"]
[Annotator "Practice"]
[PlyCount "23"]
1. e4 e6 2. Nf3 d5 3. Nc3 c5 4. exd5 exd5 5. Bb5+ Nc6 6. Qe2+ Be7 (6... Ne7 7. Ne5 Qd6 8. d4 cxd4 9. Bf4 dxc3 10. Nxc6 cxb2 11. Rd1 Qxf4 12. Nxe7+ Kd8 13. Nxd5 Bb4+ 14. Nxb4+ Kc7 15. Nd5+ Kb8 16. Nxf4 a6 17. Qe5+ Ka7 18. Be2 f6 19. Qxb2 Bf5 20. Rb1 Rab8 21. Qb6+ Ka8 22. Bxa6 Be4 23. Ne6 Rhc8 24. Nc7+ Rxc7 25. Qxc7 Re8 26. Be2 Bc6 27. Rb3 {1-0 Mackenzie-Beilin, 2008}) 7. Ne5 Qd6 8. d4 cxd4 9. Bf4 dxc3 10. Nxc6 Qxf4 11. Nxe7+ Kf8 12. Ng6+ 1-0
Following 1.e4 c5 2.Nc3 e6 3.Nf3 Nc6! White should play 4.d4 or 4.Bb5!? since 4.g3?! is not so good due to 4...d5! 5.exd5 exd5 and Bg4 will be annoying.
Joel Benjamin's "Anti-Sicilian" series at Jeremy Silman's old site is very interesting:
http://www.jeremysilman.com/chess_opng_shrtcts/archive.html The whole repertoire may interest you, but see especially parts four through eight for dealing with an early ...e6.
Against 3...Nc6 Benjamin advocates 4.Bb5!? (I prefer the simple 4.d4 now though I've tried 4.Bb5), and against the 3...a6 set-up -- where Black plays for an early b5 and Bb7 pressuring the e4 pawn -- he advocates a Closed line (with Nf3), playing d3 to defend the pawn and going for the f4 break by playing Ng5 (and then to h3 if necessary).
I'm not crazy about that, so I have analyzed the d4 lines where White fianchettoes the Bishop and sacs the e-pawn if necessary, as played by Tal and more recently by Gad Guseinov:
http://www.kenilworthchessclub.org/kenilworthian/2006/12/two-knights-sicilian-pa... http://www.kenilworthchessclub.org/games/java/2006/anti-paulsen.htm http://www.kenilworthchessclub.org/kenilworthian/2007/08/richard-pallisers-fight... http://www.kenilworthchessclub.org/games/java/2007/anti-paulsen.htm In comments to the last blog post, ChessPub member Katar suggested some very interesting improvements for White.
Hope that helps. But 2...e6! has really made me wonder why I don't just play the Open lines directly:
http://www.kenilworthchessclub.org/kenilworthian/2010/01/five-easy-pieces-open-s...