My personal favorites are the AMG, the Vette, the Aston, and the Hyundai.
The Vette and Aston are fairly stable cars, with good top speed and acceleration. The Vette can be good on fuel if you are short shifting it as you should (it starts to lose torque early and requires short shifting to be as quick as possible imo). The Aston, as stated, can slide around a bit in 2nd, but it's manageable, esp. if you use TC 2. The Astons (GT3 and 4) took me to quite a decent FIA season while we were still having the true season.
The Merc and Hyundai are not quite as fast in a straight (or at least don't feel like it to me) but are both very stable and easy to drive. The Hyundai may be one of the easiest GT3 cars in the game to drive (again, personal opinion). I'm not sure how either of these 2 cars are on fuel, as I haven't done enough fuel/tire wear races with them to get a good idea, but the Hyundai at least seems to be good on fuel with just a tad of short shifting.