What is the best trigger for the AR-15 and which is better 1in7 or 1in9 twist?

I don't have personal experience but everyone seems to be on the same page about the Jewell and RRA 2 stage triggers. Those two seem to be the most liked on the board. Devl recomended Accuracy Speaks to me for a single stage.

a 1:9 rate of twist is good but if you what to shoot loads over 69 grains, go with the 1:7.
Bushmater is taking order on a 1:7 HBAR carbine (200 orders needed) if you're interested. check it out. More info can be found in the Industry Fourm under Bushmaster. The tread is pinned to the top.
Hope this helps
Ants
 

1/7 allows use of the superior 75 and 77 grain rounds.  If you dont plan on using them 1/9 is fine.

The only two triggers I can reccomend are the Accuracy Speaks single stage and the Knight's Armament 2 stage.  The KAC is much better than the RRA 2 stage.  I have never tried a Jewel but it has even more set screws than the KAC.

I would like to take this discussion a bit farther... What type of accuracy can I expect with a RRA 20" varminter with a 1 in 8 twist shooting a 50 grain ballistic tip type bullet?

Single Stage - Accuracy Speaks, 2-stage - KAC, budget minded 2 stage - RRA tuned by John Hollinger, for the broke - the 15 minute trigger job

As for barrel, perhaps you can split the difference - 1:8.  I use 1/7 but built a beater with 1:9 cause I am only going to shoot cheap 55gr fodder in it.

The JP trigger is nice.  Has set screws, but mine haven't loosened up on me yet (they're loc-tited).  Was about 2-2.5lb until I put the stock hammer spring back in to make it work with a .22 kit.  Now it's about 4lb.

General consensus here seems to be:

2-stage:
KAC if you can afford it
RRA if you can't
Jewell if you like to adjust it

single-stage:
Accuracy Speaks on a weapon
JP on a "game gun"
15-minute trigger job if you can't afford those.  
JARD if you need it really light (< 2lb)