Well, you can only have two primary tradeskills; so, theoretically, you could be a Tailor/Leatherworker. The problem is, without skinning as a second skill, you'll have no way to get the materials you need for Leatherworking, short of buying them for inflated prices off the AH.
The main combinations of crafts (and remember, you can only have two) go like this:
Skinning/Leatherworking
Skinning/Tailoring (not necessary, but it can help a little)
Herbalism/Alchemy
Mining/Engineering
Mining/Blacksmithing
Anything/Enchanting (Many people go with tailoring, since you can make your own green+ quality items to disenchant; others go with a gathering profession like mining to help pay for the expensive items to disenchant. I do not reccomend Enchanting on your first character; it is the only tradeskill like FFXI, where you lose a ton of money to get a good profit later on. You'll lose more than most, since you can't sell equipment, and come level 40, you won't have money for a mount).
The secondary skills, first aid, cooking, and fishing, all cap out at 300, and you can get all of them. Fishing can technically get as high as 425 or so, but that's using a rod, enchantments, and lures.
Of the secondary skills, the usefulness depends entirely on your class, your primary skills, and what you like to do. If you are a melee class with no healing, or a Hunter with a pet, fishing/cooking go well together. All classes benefit from First Aid, but many seem to skip it, especially healing classes. Personally, I think First Aid is very important. Fishing is important for alchemists as well, since three fish are used for potions.
Hope that helps, have fun ^_^