Quality shared hosting should be more than enough for moving from wordpress.com-hosted to self hosted.
I'd do the maths on your bandwidth usage first to ensure that you have allowed enough, and I'd also install one of the two caching plugins - either WP Supercache or WP Totalcache (Supercache is easier).
Backups could be done with sitebackup.com or with one of the many wordpress plugins that do backups - you'll need to look through them and work out what suits you best. Most hosts will do backups, but you should also do your own as problems with backups occur regularly. I'd also do a periodioc manual download of your site, just to be sure.
Some hosts will do a migration as well, some for $ and some for free.
To minimize downtime, I'd be looking at reducing the TTL on your domain so it switches over more rapidly. I'd also look at disabling comments on your old site just before the move, and when it's been moved for a day or so, switching your old site to a maintenance page, just to avoid confusion. Other than that, if it's just a straight blog, I don't see downtime being an issue.