Kazaam, I don't know if I have any particular advice for a Mage but I'll give it a shot. I recently helped a good friend get started and here are some of the tips I gave him.
- After Riverwood, head to Whiterun to do the main story's quests and then head over to The College of Winterhold. Talk to various people in Riverwood and Whiterun, especially at the Inns, and someone will give you a quest to visit the college. Once there you can join the college and run that entire quest chain--the loot is great and you get some really awesome stuff.
- Once you're done with the college and begin doing whatever you feel, don't fast travel, use a carriage or ride a horse. It sounds nuts, I know, but doing any of these looses the opportunity of serendipity. There is SO MUCH content sprinkled throughout Skyrim and doing any of those forfeits the opportunity of exploration and discovery. Even a horse just gets in the way of it all.
- Get good at using the Ward spell.
- If you're going to be evil, get good at lockpicking and sneaking because you can get wealthy very quickly by sneaking into peoples homes, especially if you visit the rich city of Solitude. Heck, even pickpocketing is super-rewarding in terms of gold.
- Invest in Enchanting very early on. Once you reach 100 you can enchant an item with two abilities! But if you're interested in leveling Enchanting quickly just use soul gems (sold or found all over the world). Plus the trainers at the College are a REALLY great source too. Just purchase some empty soul gems and then head out questing with Soul Trap to kill enemies and fill the gems. Until you’re level 100, just use crappy items and the smallest soul gems.
Oh and one more thing, anything you double-enchant will sell for considerably more!
-If you’re running through the wilderness and you see an icon resembling a dragon appear on your compass--check it out. There be a dragon ahead matey! ALSO, there will be a new Shout for you to learn as well, PLUS a treasure chest with some awesome loot.
- Keep in mind Magic skills only gain experience if an enemy is around, even restoration spells
- If you have a ton of stuff to sell, I found the Blacksmith (two vendors) and general goods guy in Whiterun to be the most efficient way of selling things. Though the vendors have a finite amount of money, just wait for 48 hours and their pool will be replenished. This is how I got rid of 600lbs of dragon bones and scales.
- There are only two people in the world who will buy stolen stuff (Winterhold/Riften), however if you get your speech skill high enough any vendor will buy stolen goods.
- Last and most importantly, explore the world as you please. These are mere suggesting, and Skyrim is probably the most adaptive worlds every created. Whatever direction you decide to go at the crossroads, you're guaranteed to have a great time.