To make life simple, I would install on the new server the same version of subversion server that you were using on the old box, even if it is not the latest version, and upgrade later once you have the data in place.
If the repository is the
fsfs repository type, then you can just mount the repository and it will work, since fsfs is portable across OS and cpu architectures.
If you were using
bdb, then you will need to ensure the target machine has the same OS and architecture, since bdb is not portable across environments. Even if you just us a machine of the same OS/architecture temporarily just to mount the repo so you can do a
svnadmin dump to dump the contents of the repo in a text format, whch you can then load on your ultmate target machine without worrying about OS and architecture. (The dump format is portable across OS, architecture and svn version.)
See Strategies for Repository Deployment, which discusses portability of the various subversion repository types (bdb/fsfs).
Once svnserve is up and runing, hosting your repository, existing clients will need to relocate their working copies, using
svn switch -relocate <old-url> <new-url>.