I would definitely recommend installing to a new server.

It is safest to assume that any new SQL version has changes to the RS Catalog database, so do not plan on restoring a backup of your old RS DBs to your new server (also don't to a detatch/attach of the old DB). Instead, get hold of RSScripter from sqldbatips and use this to migrate all your RS objects to the new database.

When you have migrated all your objects, test that everything works as expected. You can then swap your new server into live and take the old server out of live use.