My big boys always ride in my 70cm Dollmore carrier with a giant fluffy pillow over them. They're really way too big and heavy for me to carry them any other way. I have an MSD carrier that I snagged a few years back that I usually use for my MSD boys, but it's a bit small so if I'm taking more than one I sometimes use the bigger carrier for them as well. For tinies...it depends. I sometimes wrap them in a thick scarf and tuck them into a purse, (I do this a lot with Peapod, my little BBB Nissa). Tussels, my Glati actually came with a nifty padded zipper pouch, so he gets tucked in there for travel.
I don't really use face protectors...although I really should start.
My 1/6 vinyls usually get popped into a pocket or purse with their arms tucked over the edge so they can wave at people