Factory 240 grainers should be fine, I had really good results with the Winchester 250 grain Partition golds from my Ruger SBH, I also used the Cor@Bon 260 grain Bonded Core HP's (which in truth is more than is necessary). The Winchester's I feel good about out to 100 yards, the Cor@Bon's should give you another 25 yards or so of usable trajectory. With a 2x scope I'd say limit yourself to a 100 yard shot, and practice and you'll be in good shape for any whitetail that comes along. One other bit of advice, getting a rest (portable monopod, or stand mounted shooting rest) will be the best thing you can do for handgun hunting, it will save you a lot of time and frustration. Watch out though you might get hooked on the short-barrel stuff and the next thing you know you'll be pricing a TC Encore.

Gordon