Any choice of two from Blacksmithing, Jewelcrafting and Engineering is ideal for getting the most of your professions.
While the bonuses for most professions are, item points wise, the same, Blacksmithing and Jewelcrafting will allow you the most flexible choice of bonuses.
(Mining gives you a flat stamina bonus which is good for tanks, but only for tanks, really. Leatherworking gives you a bonus that isn't too usefull for tanks.)
I added engineering to the list because it has unique bonuses that can be quite good to have, there will forever be debate about this, though.
All gear that you can buy or make will be replaced eventually, and it's quite possible to make money using crafting professions. I'd dump leatherworking first (from what I've seen the market is rather full of the mats, and the bonus is the least usefull) and grab blacksmithing or jewelcrafting. You won't have to buy your stuff from the AH then, you'll be able to craft it yourself, and both work nicely together with mining.
Once you are a bit geared up and have a comfortable amount of money, drop mining as well and pick up one of the professions you don't yet have.
Of course, keeping mining is a perfectly valid choice, and I'd pick up either Jewelcrafting or Blacksmithing to go with it. While Engineering is a valid choice, picking it up would depend on your raid group having an engineer already (the first engineer in a raid group adds a nice amount of utility, the second and third relatively little.) Engineering also isn't as flexible as the other two.
Which one you should pick up I cannot tell you, pick whichever you like better, they are equally strong as far as I know.
Getting the top-end recipes for JC is slow - you will have to do four dailies per recipe or spend a lot of money/titanium ore on it. Getting the top-end recipes for Blacksmithing can be slow - they are raid drops from some of the harder raids.
While levelling your alt, keep all the ore and bars you find. You'll need quite a lot of mats to get your professions up, and from my experiences prices are low when you want to sell stuf, but high when you want to buy stuff.