Well it's totally up to you. If you want to be an enchanter/tailor go for it, just be aware that you will be broke all the time :) They can be fairly expensive to level up if you buy the mats from the auction house. If you get all the mats yourself, especially for enchanting, that means you won't be selling any of the green items you get on the auction house. It is definitely possible to make money with the combo by tailoring green items and disenchanting them to sell/level enchanting but it takes more work.
My first character took herbalism and skinning and never had a problem with money. My second character is a tailor/enchanter but was helped out a lot by my main character sending her money. If I was to start a new character on a different server right now, I would go with mining and skinning. Mining should make you quite a bit of money right now as people level up jewelcrafting with the expansion. Skinning is great for leveling as you kill a lot of mobs you can skin. It doesn't bring in tonnes of money, but it's constant. Once you're higher level and have a stash of gold saved, you can always then drop either mining or skinning and pick up blacksmithing, engineering, jewelcrafting or leatherworking (whichever is complimented by the gathering skill you chose to keep).
Just my 2 cents :) Oh, and level fishing when you're bored. Something else that can bring in decent cash once you work on it a bit.