You can get a PS3 with GT6 for pretty cheap nowadays but if you want a futureproof solution, I'd suggest getting a PS4 or an Xbox One.
GT6 is a circuit racer with tons of cars (though most of them are really low quality). They have a great collection of real-world tracks and some of the best fantasy tracks in car game history. Sadly it's a tad repetitive imho and I'd describe it more as a car collecting simulator :/ It does have weather effects and (partly) great graphics though.
If you get a PS4, you don't have many options yet, pretty much the only notable option being the (apparently) pretty mediocre Driveclub (which has great graphics, weather effects are inbound but is apparently repetitive, buggy and the car list isn't that huge. Don't know much about it so I'd suggest googling tbh). GT7 is inbound 2015/2016 and it's likely to improve from GT6. If you can wait that long to see what it has to give, it's surely a worthy option.
Then there's the Xbox One. It does have Forza Motorsport 5 and Forza Horizon 2. Forza 5 is more like a competitor to Gran Turismo with circuit racing and lots of cars (though nowhere near GT's car amounts, they're all top-quality when compared to GT's standard cars). It's a bit rushed but does look amazing and driving is fun, but the track list is really lacking. It also doesn't have changing weather. You can get it for pretty cheap too, but the true potential lies ahead in FM6.
Forza Horizon 2, on the other hand, is an open-world racer, with a bit less cars when compared to the Forza Motorsport series but instead of the racetracks, you have a pretty big and immensely beautiful open world with both changing time of day and weather conditions. Vehicle quality and variety is great and the graphics are amazing. Now I may be a bit biased but it's definitely one of the best racing games I've played in years with fun multiplayer and tons of things to do on singleplayer as well. Only question is that is it worth the money you need to invest in an Xbox One. In my opinion, definitely the one you should be going for with how things are right now but I still wouldn't leave the rest out of the game.
Hopefully I just didn't make it harder :lol: Look into some gameplay clips on YT and reviews, they should help you decide :nods:
And if you get a next-gen console, whichever it is, be sure to get Project CARS. Huge variety in cars and tracks, amazing graphics, dynamic time of day and weather etc..