That really depends on a lot of things

Don't you love those "it depends" answers! With computers though, that's more often the case than not. If you're going to download things like Windows ISO files (3 GB more or less), it takes me 20 min. to download one of those with my 24 mbps wired cable connection, so for me that's the minimum when I'm at home. For streaming video you need something fairly fast, but I can't say where the threshhold would be. For most email and web surfing, you don't need all that much, I'd think 3 mbps would probably be OK.
If you have a laptop or tablet, you could go to a motel or most fast food places and see how that works for you.

Good luck.