I took my mining/skinning up while I was lvling for cash and when I reached 60 I took blacksmithing up real quick before the expansion came out. Couldn't have timed it better either. I'm a huge blacksmithing fan, especially with the expansion the benefits for a plate wearer are unreal, but I'd hate to be lvling bs right now while the prices are shooting through the roof.
I have 3 alts, 1 as an enchanter/tailor, 1 as a skinner/leatherworker and 1 as a miner/engineer. I just started a draenai who will be my herbalist/jewelcrafter and I will change my miner/engineer to alchemist/engineer when he reaches lvl 35.
Some of the classes don't interact appropriately being on the same account since I can't, for instance, enchant my main or other alts with my enchanter since they can't be on at the same time, but I can send the mats to my main and either tip someone for the enchant or have a guildmate do it. It also helps with making things like arcanite bars and not having to wait for the guild enchanter to be free or spend hours on the trade channels.
You don't need to go that broad spectrum route, but I enjoy being an all-purpose member of my guild. The important thing is to pair correctly, if you decide on bs, engineering or jewelcrafting you're going to have to keep your main as a miner to help with materials and if you wanna do tailor or enchanter you can do whatever with your main as you're only gonna use him to feed stuff you get for drops to the professions. Leathercrafter of course you'll need to keep skinning on your main.
If your main is a plate wearer I suggest bs/mining main and jewelcrafting/enchanting on your alt. that way you can make jewels for sockets, rings and necklaces for stats and your own plate and weapons and an enchanter for enchanted thorium and arcanite and the like.
I don't know much about the cloth-wearer or leatherworking jobs but I think I'm smart enough to make a guess that tailor/leather and alchemy/herbalist go together well and leatherworker/skinning, jewelcrafter/mining might work.