As a warrior you have a LONG row to hoe when it comes to AOE tanking. Your tab key will be your friend and I do not envy you. I can't offer you much help since I am a DK tank and AOE threat was handed to me on a silver platter.
What I CAN offer you is this: Give one warning to folks for behavior because as the person tanking you have all the power.
If they continue to fail you place them on ignore and drop group after the 15 minute timer. They'll be waiting for a new tank for up to 20 minutes while you will have finished the next dungeon. The reason you put problem people on ignore is twofold. Firstly you will never group with a person on your ignore list. Secondly they will be waiting that much longer for a tank.
Glad to hear that your making some progress in your pursuit of what is aurguably the most thankless job in WoW. Like most of the vets here I have played since the Closed Beta days, (thats closed beta for vanillia not wolk ) In all that time I have tried to help lots of up and comers in the various guilds I have been in work through what your working through. Gearwise I can't really help more then TankSpot already can. I can make a few suggestions that I make to others when they ask me about learning/starting to tank.
1. Know everything about the encounters. To me this is #1 in the books to striving to be a good tank. Rotations and theorycrafting ect help, but knowing everything about what should happen, what will happen and what could happen always helps more. Knowing the in's and outs of the boss'es as well as the trash and mechanics that strain threat, or disregard it all together and how to compensate for it will help you in many ways. As the tank..aka "the leader" in most cases.. its our responsibility to give direction, make the changes when things go wrong and be adaptive.
2. Threat Plates. I suggest this mod to all new tanks I meet. This mod will customize your target name plates to grow in size when you have little to know agro on them. This is very helpful especially as a War since it does take considerably more practice to tank 4+ mobs at once effectively then say a paladin or dk.
3. Maintain that good attitude. Tanks of all ilk like so many have said are going to be the scapegoat for a instance/raids failure. It comes with the territory. You definately seem to have a really good attitude and I hope you can maintain it. A lot of new tanks are thrown into the deep end of the pool without training and expected to by Gold medalists. As long as you roll with the punches and know you can always improve and better yourself you'll become another outstanding additiona to the tank family.