There really is no limit. If you are a worshipper of the divines you wouldn't do any Daedric quests at all. If you are a worshipper of a particular Daedra the rest would be ignored and hated. A Vampire wouldn't go into temples or do quests for the Divines, least of all Arkay.
For the rest there aren't any cultures that forbid or do not use certain types of weapons or magic in general. The way it used might differ.
Most Nords distrust magic, and as such it's quite uncommon but restoration and alchemy are still accepted traits all around.
Dunmer that worship the reclamations tribunal wouldn't use necromancy, but conjuration itself is perfectly fine.
Even so, you could play a magic wielding Nord, or a Dunmer necromancer, the second would just not follow the Dunmer temple and the first would not be a real popular guy. As for what the races are most likely to use, you just have to look at the skills.
Altmer have greater potential for magic then Orcs, but that doesn't mean you can't find Orc mages that are better then Altmer mages, or Altmer warriors that are better then Orcs.