I bought a 4gb slim and Forza 4 the other day. 4gb isn't going to cut it, because half the content is on disc 2.
I had a red-ringed Xbox that hasn't worked in 5 years. I put the 20gb hdd that was in that into my slim. Of the 13 usable gb on that old hard drive, 11 of them are already dedicated to Forza 4.
About 11gb total so far after installing both discs. If you don't want to install the first disc, you don't have to, though.