You need to look at the v5.1 compatibility lists, i.e. the Operating System compatibility list for the NetBackup version on the client to see if the client in general is supported, and also check the Database Agent compatibility list for the NetBackup version on the client to see if the NetBackup Oracle agent is supported for the O/S version and Oracle verison that you are running. - i.e. the v6.x documentation will not tell you about your client compatbilities, but the v5.1 documentation will.
All v5.x clients are supported as clients to v6.0 media and master servers.
As for whether to upgrade the client to the latest MPn level, then my advice is... if you can then you should, i.e. unless there is a specific reason not to. I always read the release notes for the MPn level concerned, I know it takes a while, but there are always one or two useful things to be learnt. Remember clients cannot be higher than medias, and medias cannot be higher than masters.