You ask if it's worth it over Skinning/Leatherworking... if your character can wear leather, don't go Tailoring/Enchanting! Go with the best armor you can wear.
Anyway, enchanting is definitely worth it, but I agree with those people that say you should hold off until around level 30 or so to start it. You will need the money in the early game to train. In case you don't get me, you gather enchanting materials by disenchanting green, blue, or purple (but why!?) items, destroying the item so you cannot turn around and sell it. Also, you may find yourself buying cheap green items from the Auction House to disenchant. But later on, enchanting pays for itself. Just TRY and walk through Ironforge with being bombarded with price listings of enchantment services, anywhere from 5 silver to 10 gold or higher! Enchantments that give weapons a glow will make you a mint, but are costly to create as well.
Hopefully this helps. :)