Leveling in a duo is tough for gathering professions, since you make the other person wait while you run off to mine a node or pick some flowers. It's a pain, and I've tried to do it more than once. It is definitely worth having a gathering profession at 70, but unless you work out making each other wait, it won't level with you. I had to go back to mithril on my 64 war to get mining up to level, huge pain but worth it in the end. Skinning is nice, however, since you don't have to stop or run away from your partner to gather. Just not quite as much money.
That said, I generally pick profesions that make the best BoP items for your class. Since you said no engineering, there really isn't anything for warrior. The blacksmithing 2h weapons are about equal to, if not worse than, the s1 weapons you can buy for honor. Being able to make some BS items that sell is nice, but I don't know if its worth it. Up to you. The 1h bop weapons are good for a fury war, but you probably won't raid so its moot.
My suggestion is enchanting. It is totally worth having an enchanter, and you will be able to d/e all your items while you level, as well as when you upgrade epics at 70 to make some of your money back. Plus you get ring enchants. The profession to pair it with is totally up to you. Those engineering glasses are pretty sweet.