First up, a quick overview of the wheel support in the games you listed (and a few others):
GRiD is really dreadful with a wheel. So much so that I bought it, experienced the floatiness and steering lag (I couldn't keep a simple race car driving straight along the mulsanne straight, it was weaving all over the place). Then took the game back to the shop and swapped it. Awful.
On the other hand, DiRT 2 and DiRT 3 are huge amounts of fun with extremely good force feedback and very responsive (no steering lag), and F1 2010 is also very decent (I've not tried F1 2011 yet). So Codemasters can do FFB, they just didn't get it right with DiRT 1 and GRiD. Once you get a wheel, I recommend you download at least the DiRT 3 demo to try it out. I guarantee you'll enjoy yourself.
I tried Shift 1 on the PS3 and found some steering lag and a rather bizarre car see-saw snap effect: Didn't enjoy it very much. The PC version got a few mods to improve the steering lag, but it was still present and ruined my enjoyment of the game. I never purchased Shift 2 because there were too many reports of worse steering lag than Shift 1 had.
GT5 of course has no steering lag or floatiness. FFB is excellent.
Regarding wheel wobble in GT5 - there are two types:
(1) When driving a really fast car (X2010, FGT) above say 300kmh, the wheel starts to wobble quite violently when you're dead straight. This is a simulated effect, basically, you just have to hang on and keep the car on the track just like a real driver would need to do at those speeds. If you keep the wheel fractionally offcentre it becomes easier, and driving the X2010 encourages you to lower FFB (hitting a curb while driving with a decent wheel set to high FFB settings will attempt to rip your arm off).
(2) With pretty much any car, if you drive in a straight line and take your hands off the wheel it will start oscillating left/right/left/right, see-sawing. This really isn't a function of any particular wheel, it's the game. It is more pronounced on my Fanatec GT2 and my G25 than my DFGT, though. To be very clear: That same Fanatec GT2 has no see-sawing effect when playing Forza 4 on the XBox. It's not inherent to the wheel.
One comment which must be made: You have a PS3 and are willing to spend quite a lot of money on a wheel, and you pretty much only drive street car simulation games. Make absolutely certain that you are not going to want to also drive Forza 4 before you choose your wheel. Only the Fanatec wheels have XBox and PS3 compatibility, so if you start itching to play Forza (which I recommend: It's far better than Shift 1/2 and easily in the same league as GT5, just different strengths) you might regret purchasing a PS3 only wheel.