Wall of text incoming.
As a mage early on there are two things to think about:
Destruction damage(which sucks), and Destruction leveling(which also sucks).
Given that, you probably want to choose a race with a bonus to destruction, since conjuratoin, as stated above, is pretty easy to level.
Dark Elves are a great choice because they start with 25 destruction, meaning you can spend your first two perks on novice and apprentice destruction and reasonably use tier 2 spells, plus you're closer to the damage increase perks and impact. They also get an additional spell to start: spark, though you can pick up the spell tome for that in Helgen. They don't get a boost to any weapon skills. Their racial resistance is decent and their ability can help in the lower levels of play.
High Elves are another great option as they get a starting 20 to all magic skills, but that's all they get. Combined with the highest starting magicka and their racial ability giving them insane magic regen during OH pl*ps moments.
As argued above Redguards also get a starting 20 to destruction, as well as a 25 in 1-handed weapons so they are no slouch in melee. Given that their racial ability is insane stamina regen they can stick it out in melee in OH pl*ps situations or run away and just keep on running.
Imperials are a fabulous choice. They get 20 destruction and 25 restoration(arguably the hardest skill to level in the game) and they get a 20 in 1-handed and heavy armor so they can survive alot more and do decent damage in melee. Their racial ability is a once a day panic button that can make enemies stop trying to kill you so you can get the hell out of there.
Orcs do need to be mentioned. They get both 1-handed and 2-handed bonuses as well as a 25 in heavy armor so they are easily one of if not the best melee race out of the gate. As far as magic goes they have very little to help them out, but there is one thing that is a BIG help. Orc's berserk racial ability halves the damage you take and doubles ALL damage that you do. This applies to magic as well so your destruction spells damage doesn't suck nearly as bad AND you'll die alot slower in OH pl*ps situations. You might even turn certain defeat into epic victory with it.
If I was rating them, it'd be:
1.Dark Elves
2.High Elves
3.Imperials
4.Redguards
5.(or1)Orcs
An orc would be the best in theory simply because berserk is that good, but as a mage and because leveling destruction is semi-painful, they come in last. Do yourself a favor and take a dark elf for a spin. Weapon skills and conjuration level easily enough through use, but destruction help early is a BIG BIG plus. Too big to be edged out by a high elf's magicka bonuses.
I did not mention Bretons in this list. There's a reason for that. They get no boost to destruction, and no boost to any weapon skills. They get a good boost to conjuration, but really guys, conjuration levels SO easily just through use, it's probably the second fastest thing to level in the game(playing naturally). Being gimped offensively is horrible in the early levels and leveling slowly is going to make that even more painful. On top of that, their racial abilities are only useful against other mages and dragons, and neither of those are what usually kill mage characters. What kills mage characters is frustration during the early levels because every enemy stronger than a wolf can destroy you.
