It's a pretty big jump from games like those you listed to Assetto Corsa.
First thing you might want to do, download RaceRoom Racing Experience.
http://store.steampowered.com/app/211500/
It's "free" to play, which really means that you get a little bit of content to play, and the rest you pay through the nose for. But it does give you a chance to try a relatively modern simulation type game to see what it feels like to you.
Assetto Corsa is probably even stronger on the simulation type than RRRE is, but at least RRRE is in the right ball park.
If you have friends that can lend you either a PS3 and a copy of Gran Turismo, an Xbox 360 and a copy of Forza or an Xbox 1 and a copy of Forza then that would be a good thing to try too. Forza 5 is a long, long way from Forza 1.
If you enjoy that, then maybe you could look at getting AC, or you might want to pick up some of the older sim titles first. GT Legends, GTR2, Race '07 and all it's endless addon packs can all be found pretty cheaply. Graphically they're OK, not great, but they're still decent simulation games. F1 2010 through 2013 if you like Formula 1.
I wouldn't rush into getting Assetto Corsa. It's still being developed, and it's bound to be cheap again soon. If you haven't got a wheel, make sure you've at least got a good gamepad to play with. Assetto Corsa is also a bit light on gameplay at the moment, so I'd recommend something like Gran Turismo or Forza or even Grid: Autosport as a good place to start before moving on to Assetto Corsa.
If you've got a wheel, and you've got a good amount of experience driving a real car quickly, then maybe jump straight into AC. Otherwise, I'd say build up to it, you'll have more fun that way.