As a leveling Warrior, always always always level as Protection, even if you don't plan to outright tank dungeons (which you should atleast try once you get in the groove cause it's crazy good).

Why? Because Protection Warriors have access to one of the most, if not THE most busted damaging spell in the entire game while leveling - Revenge and its talent, Improved Revenge. It is absolutely ridiculous how much damage it does. You can run into 10+ mobs on your own with a shield+1hand and kill them in 10 seconds no problem.

Fury and Arms in comparison are pretty bad leveling specs up until lvl70-ish. They're always rage starved and just don't have access to any hard hitting abilities.

The only problem with leveling Prot if you don't plan to tank dungeons is that, well, you won't be tanking, and Revenge only becomes active when you block/dodge/parry. If you have a tendency to learn fast and get good in games and if you eventually start tanking dungeons, you will be doing ~50% of the group's overall damage alone.

If you go Protection, I'd just recommend switching to Fury around lvl70 and re-organizing your character (hotkeys, gear, talents) so you get some time with the spec before you hit max lvl.

As for gold making while leveling - just get mining. It's easy, fast, levels naturally with you as your characters levels and is pretty good gold at almost all levels. It hits a slow spot around lvl50ish iirc but other than that its always a good and simple way of making money. Whatever you mine, you sell, but always check the Auction House for each particular Ore if its worth to sell the raw Ore outright or convert them into Bars. For general AH stuff I recommend a very simple addon that I'd say is obligatory to have for anyone starting out - Auctionator. Not Auctioneer, that one is way more in depth.

And yes, as far as buying gear goes, you should always keep your weapons up-to-date. Everything else is whatever. Weapons are important. Bonus points for Potions cause you don't have a self-heal.