I've never played any Elder Scrolls games either. (I tried Skyrim, but didn't inhale).
In ESO, there are 4 classes. But all classes can wield magic (or not, if you choose). All classes can wear light, medium, or heavy armor. This means you can have classes like a rogue or mage who tank. Or a tank who can heal. Or a healer who focuses on melee dps.
The four clases in ESO are Dragon Knight, Templar, Sorcerer, and Night Blade. Each class has 3 "trees" to help define your class.
If you want to be a mage/wizard, I would suggest playing the Sorcerer. The 3 sorcerer trees are: Dark Magic, Daedric Summoning, and Storm Calling. Eventually, you will have enough points to spend in all 3 trees. For the typical mage/wizard flavor, I would recommend going Storm Calling, with 1 or 2 points in Dark Magic).
Keep in mind, you also want to focus on what race will compliment your chosen class. Each race has unique racial abilities that will grant you increased experience. For example, if you play the Breton race, you will have magica increased by 4%, reduce magica cost by 1%, increase spell resist by 2%, and increase experience gained by wearing light armor by 15%.
Compare this to the Altmer (High Elf) race. High elves get magica increased by 4%, magica recovery in combat by 3%, increased damage with cold, fire, or shock by 2%, and increased experience with a destruction staff by 15%.
There are lots of Class - Race - Skill combinations that are intriguing.
For me, an altaholic, I've been experimenting. I fell in love with the Orc Dragon Knight who focuses on Ardent Flame magic. It's a tanky-mage-healer (if you equip a restoration staff and pump points into Magicka).
All classes can equip the restoration staff, which gives you basic healing abilities. However, the Templar class, has a dedicated healing tree, which gives you much better healing.
With ESO, your imagination is the limit to what you want to play and how you want to play :)