I would migrate the blog AS-IS in 1.5.x (files and db), make 100% sure it safe on the new server, then back it up again and follow upgrade procedure to 2.2.
I recently did both of the above, and I made some mistakes that costed me a lot of time, but was ultimately quick fixes when I figured it out with lots of threads and help from here. Point is, there's a lot of potential complications to both moving and upgrading, although neither should be that difficult. Take it step by step, don't pile both on the same instant.
those tamba2 guides are great, although I haven't seen if there is one specifically dealing with the 2.2 upgrade. Great resource for moving servers.
also what charlie and moshu said