So is base set professor oak under the same restriction as juniper and sycamore?
The special rule about not being able to run
Professor Juniper and
Professor Sycamore in the same deck is exclusive to them. You may run four
Professor Oak alongside either
Professor Juniper or
Professor Sycamore, just
not both.
Professor Oak counts as an Item card because it was released as a "normal Trainer" and never anything else. The same is true of cards like
Professor Elm,
Erika, etc. Even though they feature specific characters and have effects that would be reserved for Supporters nowadays, they are classified as Item cards.
The reason that doesn't apply to an older card like
Bill as well is simply because
Bill was
re-released as a Supporter. This means all past versions are either illegal to use or played as if they read the same as the Supporter version. I am not sure which is the correct ruling about older copies of
Bill because I think this has changed over the years (like the rules about foreign language cards). Sometimes, the latest printing of a card overwrites minor changes to past versions, but this is a pretty significant change, and when that happens, usually only the latest version is legal. If that is the case, then someone wishing to use
Bill in the Unlimited Format would have to track down its release as
Heart Gold/SoulSilver 89/124.
Also I was gonna pick up some reverse holo admins to replace n in my unlimited deck but you cant find them anywhere, the only ones you can find are the world championship ones
If you aren't worried about forcing your opponent to deck out or
are worried about decking out yourself/have some combo with Team Rocket cards (I can't remember if any such support exists that would apply to Supporter) then you might "need" to splurge for
Rocket's Admin. If not, then you should be just fine with
N. If you want to force someone to deck out, then you'll
need the
N.
Good luck.