Who is the best?
That depends on what you need. Pair, as mentioned above, is great for dedicated servers...I haven't used their shared hosting, but I would imagine that is fine as well. Bluehost is great if you can live with their TOS...read it carefully, especially the parts about bad language. Liquidweb is excellent, but a little more expensive than most.
How easy is it to get things switched over?
Not difficult. See videos at link below.
Whatever you do, get a linux account and I would personally recommend getting an account with Cpanel...makes management infinitely simpler.