I helped many clients do this and i will also move the database and re direct your domain name to ensure that it is all working.
I actually have a full tutorial so you can do it yourself if you need to do it again - Please refer to gig extras to find out more....
- All logins for cpanel and domain name servers required
- quickest job with cPanel
- Moving folder locations within current hosting
- Moving to another domain and hosting
Can chat about cheap fast domain hosting if needed :)