For brushes I'm sure everyone does it different. Since your just wanting to clean him up and do some bonding, heres what I do.
I start with the mane and tail. You can just use a human hair brush on that I like a pretty stiff vent brush. Granted the good mane and tail brushes last longer but they are expensive. The cheap ones don't work as well as the human vent brush imo.
Then the curry to knock off any stuck on mud. If you get a metal curry don't use it on the bony parts except to do it VERY gently to knock off mud.
Then a pretty stiff bristled brush worked like a broom in a sort of short flicking motion to bring up any deep dirt. This is what I use to get any mud off the bony parts and legs.
I then go to a little less stiff brush and continue brushing with the flicking motion except in longer strokes.
I finish by brushing mane and tail again then use a soft finish brush to lay the hair down. Don't flick with this one just long strokes in the direction off the hair growth.
I use an old towel if there is still a lot of dust, just to wipe them down.
I have a black horse so she always looks a little dusty no matter how much I bush unless she's had a bath. Or I spend hours brushing which I don't
If he's extra dirty and you don't have the means to give him a bath, just take a bucket of water with you and dip the brush in the water.
This is just my procedure. I'm no groom I'm sure I forgot something
Have fun, this is my favorite part of having horses.
If you want to get fancy they sell small face brushes, again going from stiff to soft. I think some human baby brushes would work just as well. My horse loves having a very soft face brush run over her closed eyes.
Just want to add I'm sure you know this but never work around a horse in open toed shoes. Always wear good foot protection. A horses hoof can do real damage to your feet (speaking from experience) They don't do it on purpose but they stomp for flys or whatever and I have the bruised toe nails to prove it