What type or how good of an internet connection do you need?

This is really a function of how much data you have to backup and what your upload speed is.  Note that it's the upload NOT the download that matters.

Most ISP's will offer much quicker download speed than upload speed.  A typical home cable internet connection will be something like 20M down and 2M up.

You can test your speed here .  So.... dialup is out!  Most 4G, DSL, and cable connections are fine. It's simply a matter of how much data you have.  If you have a very large amount of data you may want to consider initial seeding.