the best advice is to google your states requirements. Every state is different. When I lived in nevada, we considered doing the branding thing and our state would let you design your own brand. Obviously there were requirments on size and shape (so the brand wouldnt blur) and you had to go online to see what brand designs were taken.
In states where there arent any brand inspections it seems like brands arent too much of a deterant if someone wants your horse- you dont even have to have paperwork on the brand if you run them through an auction (unless its a mustang).... where as in nevada, if they pulled you over with a trailer and you had a branded horse with no paper work, they could and would confiscate that horse until you provided the appropriate paperwork..
as for micro chipping, those chips dont come standard and unless you have a reader that will read the chip implanted (pretty common)- they can be pretty useless.