I have a bay and white paint also. My curry is always dirty, just tap it on something when you see you're just moving the dirt around instead of removing it. IE: pavement, fence, your hand.
When bathing its nice to start at the hoof/leg so the temperature doesnt shock them. I wet my horse well, shampoo his entire body ( i use mane/tail shampoo for body and mane/tail) then I use Goop, see the post about getting a yellow horse white . You can buy it in the automotive section, its for mechanics to wash their hands, but I use it on mane and tail and any stained spots.
As far as picking out the hoof, google the anatomy, its important that you clean it properly and that you have confidence. Any lack of confidence MAY end of causing your horse to not trust you, which can turn into disrespect. Not saying it wil, but it happens with newbies. Find someone knowledgeable and see if their willig to work with you, it'll help build your confidence tons.