Oh. I don't know any easy ways to make money quick, but Transmutation should be useful anyway, either from selling the resulting gold directly or from selling the jewelry you make with it.
There are probably a lot of side quests and miscellaneous quests with good money rewards, but I don't pay attention to the money so I don't know which is most efficient. I've never played with the standard UI, but I hope there's a way to sort all your items by price. Should give you a good idea of what's worth picking up. Most armour weighs too much I find. Elven and glass probably have the best weight to value ratio. Magic staves are pretty good. And then all the small stuff of course. Potions, jewelry, gems, ingots. Maybe rare furs, but I stopped picking them up, so I don't know.
Pickpocket 50 gives you access to Extra Pockets (100 more carrying capacity). Should be very useful for any character. Uesp.net should have a list of all Pickpocket trainers to make leveling easier.
Honestly, quests are probably your best bet. Uesp.net should be able to point you in the right direction there.