Races are up to you. I haven't played in a while, so I can't remember bonuses specifically. However, I remember something about a sign that gets regeneration to mana at the cost of being more exposed to fire - well worth it if you ask me. But if not, try finding those races, classes, and signs that just give mana bonuses. Remember though, the higher the mana they give, the more likely they have a weakness to balance it out.
Well, for good mage, you'll definitely want to join Mage Guild ASAP. Most spells you buy are crap (And that's what you should buy, crappiest version of each spell so you make a better version). If you have Frostcrag expansion though, don't worry about Mage Guild too much.
Second, consider what kind of mage you are going for. If you want a summoner, then focus on Conjuration, if you want a Battlemage, perhaps split focus between Conjuration and Destruction - for magic armor and offensive magic. However, magic like Unlock and Burden are very very useless, so be careful with what magic you THINK you want to use.
But remember this, you are a mage - some defensive magic or alchemy will do you a whole lot of good, though your alchemy should be maxed already since it's so useful. Invisibility, defense buffs, healing especially.
Anyhow, when making offensive spells(Shock, Frost, or Fire), try to get two kinds.
1.Bang for your buck. Make a one target spell that deals a LOT of damage. You have two options with this. Make it deal Damage Over Time - which deals more damage over a long period of time, so you can use a bow or something. Or you can just deal one second of it, which will drain your mana much more heavily.
2.Large area. This is when you're being gained on by lots of pesks, they can become costly though, so use sparingly.
Don't put aside Conjuration though, the summons are good tanks if you want to keep your distance from the enemy. The armor is also decent, since if you're a mage, you won't have much room for strength, and the armor is weightless.
If you're running the PC version, I suggest you go to www.tesnexus.com and search up MIDAS MAGIC or something like that, should be in the top 100. It adds literally HUNDREDS of new and mostly unique spells and quests. You can summon a tiger to ride and attack people.