As far as actual legality goes, the only cards legal to have in your deck are Momir Vig, Simic Visionary, as well as Plains, Island, Swamp, Mountain, and Forest.
This is hinted at on the Wizards page, as well as stated clearly in this article:
(...) your deck contains 61 cards. One is the Momir Vig, Simic Visionary Avatar and the other 60 cards are basic lands. (...)
For cards to be randomly chosen, this article describes it as follows (original links omitted):
(...) the random creature you get is picked from the entire Online Classic card pool. This even includes premium cards from sets that have not been released online, such as Preacher from The Dark, or Serra Avatar from Urza's Saga.
Naturally, this only applies to games on MTGO - if you play Momir Basic any other way (for example using a random generator like MTG Familiar to determine the random creatures), no particular limits apply, and your group of players should decide which cards or editions to exclude, and whether to allow cards that are banned in certain formats.