Question about T-Mobile W/ iPhone.?

I currently have T-Mobile, and I want to get a iPhone, AT&T is a lot more expensive, so I was wondering if it was possible to unlock it, and still have it work the same as it would with AT&T. I know that with unlocked phones, there are bugs and stuff with the texting, but I was wondering if the apps, and internet will work the same.

Also, will the internet be slower with T-Mobile that it would be with AT&T? Or what's up with that?

-Thanks!