Can I use T-mobile's 4G(or 3G at least) network with unlocked AT&T Galaxy S3?

[House]

I'm trying to get a AT&T's version of unlocked Galaxy S3(Garnet Red) and use it with T-Mobile.

I am dying to know if I will be able to enjoy T-mobile's 4G network with the phone.
If not, I'd be happy to know if I can get 3G speed with their network.

Can someone please let me know please? Thank you!