If you plan to use heavy armor, join the fighters guild as soon as possible. Many of the branch offices have steel armor laying around for the taking and the main branch has 2 fine steel longswords for your use.
Abjuration makes lockpicking obsolete. Level yourself up to 75ish and you can open ANY lock without the use of lockpicks.
Illusion makes persuasion obsolete. As soon as you get into the Arcane University make a touch spell that gives 100 reaction for 1 second. Since dialogue "stops time" this allows you to use your good vibrations, talk to them and get maximum reaction for only a tiny amount of mana.
Destruction and Restoration are hard skills to gain ranks in, because to gain ranks in destruction you have to do damage to something and to gain ranks in restoration you have to heal damage. Now you could summon something and blast away at it, but the easy way is to make a spell in the Arcane University that does 1 damage to yourself and then heals yourself.
Don't pick skills that you plan on using a lot for your main skills. I realize how silly this sounds, but the faster you level up, the stronger your enemies get. However, if you pick things that you can easily control how much you use (such as locksmithing and persuasion) it's possible to be the most powerful warrior-mage in all the land and still be level 1.