How to migrate existing blog between hosts

I put up with vizaweb’s shortcomings for long enough. Last night was my 1 year renewal and idahofallz.com says my domain name expired. Their billing system says my invoice is paid, so ummm???

I’ve been sending emails for 16.5 hours now (no, not continuously) asking if the payment failed or if their payment system didn’t flow to their registrar ? Nothing but autoresponders.

So I’m looking for a new host, webhostingjury shows u2-web is decent. I like the cplanel/fantastico vizaweb had, and u2-web also has.

My question (finally sheesh) is what concerns do I need to keep in mind to migrate from one host to another? My site is down now but I can access my FTP, fortunately I backed up my site right before the domain name problem, I’ve downloaded that last backup already to my local machine. Will that backup (made through cpanel) have everything to restore at the new host?

I have a highly customized theme, 190 posts, 160 comments, about 40 registered users. I need the migration to be perfect so nobody has to reregister, no comments are lost, no posts are lost.

Any advice for doing this?