You should be able to use any reasonably sized lag bolts. As noted, just try not to put them too close to each other so that you don't split the wood. 2.5 inch should be plenty so that it doesn't go too far into the vapour barrier and insulation.
The vapour barrier will be between the drywall and the studs, so any lagbolt will penetrate the VB, although it won't be a big concern.
Use an appropriate size lag bolt. Longer doesn't necessarily mean stronger, as many longer lag bolts are only threaded partway up the shaft.
Given that you are probably using 1/2" or 5/8" drywall, a 2" to 2.5" lag bolt should be plenty.
Having the lagbolt go through the 2x10" probably won't increase the strength.
Some TV's are lighter than others. I just hung a 32" LCD in the kitchen for my wife, and it used 2 fairly thin lags (my guess is a #12 or 3/16" lag) to hold the TV to the wall. I went into the stud, so I have more purchase.