Or you could choose alchemy as a minor. Go to the Balmora Temple and raise the ingredients merchant's stock in wickwheat and saltrice by buying and selling back until you get all you can carry. Buy a mortar and pestle and find somewhere you can sleep in peace (the Seyda Neen Customs House works), and start clicking. Sell finished potions to Creeper and do again.
Brewertripper style!!!
Nice, gotta try that one out.
Or you could soultrap summoned creatures. Take Conjuration as a Major (you get Summon Ancestral Ghost.)
Get the soultrap spell.
Take the boat to Tel Branora; the vendor there sells restocking common soul gems (40 gold each.) Buy a bunch of them. Summon ghost, soultrap, and kill. Repeat. Sell the gems to the Creeper (4000 gold each.) Rinse and repeat until you have all the training money you need.
When you level up a bit, move up to grand souls (Golden Saints.) There's a vendor in Mournhold who sells them. They're 80,000 gold each, filled, or use them for enchanting.
I think it's boring, but then again, so is any kind of routine grinding.
This is surely helpful for beginners.
And for higher level characters, I think the easiest way to make a lot of money quickly is actually to frenzy kill Ordinators and sell their loot to mudcrab. 30000+ gold for each one you killed if I remember correctly, and they respawn, AND since they all got bad attitude, you don't really feel bad killing them (unless you join the Temple and they will be nice).