I have tried stealing, but the cut the fences take is overtly greedy, and I dont really understand alchemy. Smithing is just frustratingly slow to level, and enchantment seem ok, but i dont want to use magic in my thief/assassin
I also trained a thief and I was very rich. That was because that I never paid for anything.
Buy a horse - steal back the money
Train pickpocketing - steal back the money. (If you're part of the thieves' guild they won't even mind if you get in their pockets so just keep trying. This can save you A LOT of money, just make sure you train one level and then steal back the money (this way the stealing chance is higher) before training the next level.)
Guards catch you - bribe them and steal back the money.
And just steal everybody's money and stuff.
P.S. In my game, the first town is entirely shirtless :D THIEVES RULE!!
It's really kind of hard to make a living just stealing things. As a thief/assassin, stealing reagents and making potions and poisons isn't outside the realm of your roleplaying, though.
The thing to go find is Giant's Toes - there's a particularly good stash of them in the kitchen of Castle Dour in Solitude. You've probably already been to this kitchen if you've been following the assassin's guild quest line. If not, you can take the carriage to Solitude and go hunting around for the castle. (Don't confuse Castle Dour and Blue Palace, though - Blue Palace is where the Jarl is in Solitude, and not where the Toes are)
Once you get to be a world-class assassin, you can harvest them right from the source by sneaking up behind and backstabbing giants. Alternatively, you can use your rogueish charm to get in good graces with alchemy vendors, and get a good discount when you go shopping. (Or you can just break in at night and steal all the ingredients not nailed down...)
Once you've stolen a few of these, go outside of Whiterun and collect blue butterflies and blue mountain flowers. Then take your pile of all of these things and mix up some potions at an alchemy lab - in Whiterun, there's one in Dragonreach and at the alchemy vendor. Mix these three ingredients, and you'll make an extremely powerful (but extremely useless) potion. Sell it to your fences and watch the money roll right in.
Once you've done a bit of this, you can create some excellent restore health potions by mixing your excess blue mountain flowers with wheat (also available in quantity by stealing it from farms near Whiterun, it respawns after a couple of weeks) and/or "regular" butterfly wings, among other ingredients. These potions are great, given that you're going to occasionally find yourself in a scrap, where a thief/assassin is at somewhat of a disadvantage.
Once you've mastered alchemy, the world's money is your oyster. Need to be invisible for a particularly sneaky (or dirty) job? There's a potion for that! Have a short-term need for a bit of extra lockpicking skill? There's a potion for that! Want to shoot an arrow that drives your target into a rage, killing his allies? There's a potion for that too!
Have you gone through the entire Thieves Guild line? You can get a decent income from the side jobs that are given by Delvin Mallory and Vex.