First off in wow there are primary and tehre are secondary professions.
Primary are Mining, Skinning, Herb gathering, Enchanting, Engineering, Blacksmithing, Letherworking, Gem cutting, tailoring, alchemy and I might have missed one or two.
Secondary are ONLY First aid, Fishing and Cooking. you can learn all 3 at the same time, they are SECONDARY and are essential for some classes.
As to primary tou can only choose 2 but you can unlern if you want to switch but all the prgress and recepies that you have learnd will vanish if you decide to go back to it. So be carefull with unlerning.
Moving on, Most producing professions (Blacksmithing, letherworking, alchemy) need a supporting one (skinning, mining, herbgathering) some dont like tailoring and enchanting.
The best moneymakers at low level are mining (sell ore on ah) and skinning (sell skins to vendors at low levels and on AH at higher)
GL