The permissions should stay the same, depending on how they was backed up, most host panels will retain the correct permissions for the file structure.
To answer your question though, it is as you asked, dump the db, tar/zip everything up, un tar/zip on the new host, dump the db into the new db, edit the config file for the db info and you should be all set.
If you manually tar the files up, use the -p switch to retain file permissions if it doesnt do it for you automatically.
tar -czfp - tar.gz
tar -cjfp - tar.bz2
|