I'm going to create a new character and want to try a primarily magic user character. Are there any restrictions or penalties if you wear armor and cast magic as there are in some other games?

Nope.

In terms of in-game loot, clothing and light armor more frequently has magic buffs, but there are still plenty of options in heavy armor, and enchanting opens things up entirely.

Nor really. If in Heavy Armor, you'll move slower.

The Alteration perks, Mage Armor, don't work if you're wearing armor.

The penalty is through the magicka attribute that mages need to heavily level in.

By needing magicka they are unable to put a lot of levelling points into stamina meaning they are not as strong and won't be able to inflict as much damage or carry as much even when they are trained in armor and melee skills. Which makes sense as a character training in magic wouldn't have as much time to train on physical excersise as a warrior which would reflect in their body's ability.

The reverse is with a warrior & magic

With enchanting, you can make even the heaviest armor have the same bonuses as the best robes. Even better, come to think of it.

The only thing close to being considered a penalty is that you dont get the magicka regeneration speed like you get with mage robes. But with enchanting and cost reduction, you dont really need it.