Before I start, understand this: If you take a production profession, such as blacksmithing, without its corresponding gathering profession (for smiths, mining), you will spend the entire game bankrupt.
For warriors, there are four typical paths.
1) Blacksmithing+mining. Warriors are utterly gear-dependent. This combination ensures you'll have a solid baseline of gear to work with, which is important for warriors. However, it is a very hit-and-miss profession when it comes to making money. Some thing make lots of money, and some make none at all.
2) Skinning + mining/herbalism. This is the money-maker's path, avoiding the expensive production skills for the almost purely profitable gathering skills. You can skill up skinning almost without thought. Mining is more time-consuming than herbalism, but as a warrior you can offer blacksmiths materials to make stuff on commission. Mining, from what I've seen, is more profitable than herbalism, but some herbs sell very well indeed and it's easier to gather.
3) Mining + engineering. This is the preferred path for those who don't worry about money. Engineering makes lots of fun toys, but it takes quite a bit of work and materials, and very few engineering products sell. (Most have an engineering requirement to use.) Engineering gives you access to esoteric items and stuff you would never have otherwise, but you pay a price for the privelige.
4) Herbalism + alchemy. Alchemy is the ultimate clutch performer; with special-purpose potions and long-term buffs of all sorts, alchemy provides welcome boosts in the hardest of situations. It's not tremendously profitable unless you stick with it, but if you learn what sells (hint: anything that gives +Agility) you can make fair money off of it.
There you have it. Blacksmithing + mining is a good warrior's choice; alchemy is also very useful; choose engineering if money is no object, and two gathering professions if money is everything.