I just hit 53 and I was wondering if I should start trying to get some of my AA's or if I should just go for 75 and then worry about them. I have soloed pretty effectively until this point and I would like to continue as long as possible. So I guess the real question is, will AAs allow me to do so and which should I invest in first?

well, i got Run 3 and then leveled to 62 before i hit the AAs hard and am satisfied that that was a solid route. the first defensive AAs are what, level 56/59 required? and those avoidance and mitigation lines are the meat and potatoes of the warrior class.
but unlike you i was all about grouping, and i never had much patience for soloing and therefore can't recommend where next for you to solo :( i found the exp (and the conversation =P ) much more rewarding when grouping with others. but since you prefer soloing i'd recommend some offensive AA's to up your dps (Ferocity, Flurry, Double Riposte) having them will also up your aggro which will of course also come in cool if/when you group. and since when you solo it's essentially your hp bar against the mob's - those defensive AAs (in a few levels) will help you stay alive longer to kill your target.
as far as leveling to 75 before starting AAs - if you've got gear waiting for you to get the levels, you've got a chance. if not, id recommend stopping at 62 or 65 to catch up on some AAs, 100-200 if you can, and gearing up at 65/70/71. because a 75 WAR with no AAs would be like a cleric with a 500mp manapool, near impossible to solo anything OR get a group :(
playing a WAR is remarkably slow and steady going, but in a few more levels you'll be getting some game-changing disciplines (Furious & Mighty Strike for example) and things'll start looking up! have fun!

I have also found that unless you have your mitigation and avoidance AA's, you will have a tough time even at 62 in places like Halls of Honor. The mobs hit my 65 Warrior for up to 450 per ...prob average 200. This is with 11.5k hp buffed and 2.1k AC. I have started AA'n and have CA at 4 and CS at 4. With each rank added to these, I see a noticable difference in the ability to not be a mana sponge for our healer. So, I would recommend stopping to get AA's at 60, then again at 65, then again at 70. That's my route.

I do alot of grouping and people seem to be spoiled by lvl 70+ tanks with really good damage mitigation and avoidance. Then when they have a tank that doesn't, you rep starts getting poor which starts hurting you grouping opportunities. It's like tank suicide to lvl first now a days.

Just my 2 cents from what I have experienced.