I found this tune (credit to Jorday, the OP) extremely effective all-round
downforce max/max
diff 15/20/15
ride height -5/0
spring rate 16.4/17.5
damper ext 6/8
damper comp 5/7
anti roll 5/7
camber -2.5/-1.5
toe -0.25/-0.15
trans 249
brakes 4/1
Also, see this thread:
https://www.gtplanet.net/forum/showthread.php?t=147815
The FGT has few problems in high speed corners where downforce will keep it to the ground. On slow corners however, it can be tricky to keep control; the major change comes from adjusting the diff, as in the above tune, it will alow you to keep the rear end in check.
I'd advise you set your ABS to 1 and skid recovery on as well, TC doesn't matter all that much. That with the tune, will make the car agile enough, while still being very neutral under braking.
On specific races:
Fuji: tricky towards the latter part of the circuit, with lots of off-camber, slow corners (makes it ideal to practise), keeping as close as possible to the racing line really helped me here, as visibility is bad and don't try to take the last corner too fast.
Indy: Not much to say, easiest race of the series, just don't barrel into corners too fast.
Monaco: Whatever you do, stay calm and cool, drive at your own pace. The biggest danger here is getting stuck on a wall, which can take a long time to recover from. Shorten your gearing (to about 320-350 kph) and take it slow at first; don't worry, the AI is slow here too.
Nurburgring: The AI cars will seemingly be a little faster than you, but every other lap or so, they will spin out on the final chicane, giving you a fairly easy win as long as you stay on the track.
Monza: In the dry you can comfortably cut the chicanes, as well as drive over the curbs once you get the rythym. The AI cars will seem to outaccelerate you due to shorter gearing, meaning you can blast past them when you get up to speed on the straights. In the wet, check the above thread link for good suggestions on settings.
Suzuka: Mostly fast and flowing, apart from three sections where it's very easy to go in too fast: the right angle corners after the first series of fast flowing bends, the hairpin just after and the chicane at the end. Whatever you do, brake on time! Going off in any of these places will send you careering off the track facing the wrong way, make sure you don't!