As far as a tub goes, any tub with a latching lid will work. Make sure it is latch, and not just a press and lock type.
You will want a UTH for the tub, plastic and heat lamps do not mix. If you don't have a thermostat yet, you will need one as well.
Provent -a -mite, available online from Pro Products, is your best bet for the mites. As stated you can use a shallow warm water bath with a drop of dish soap or baby shampoo in it to drown some of the little buggers while you wait for your PAM to arrive.
Newspaper or paper towels while you are treating the mites is a good idea according to most.
Lastly, are you sure he isn't hissing when you pick him up ? A lot of times a nervous snake will close-mouthed hiss to protest an intrusion on it's privacy. Since you only hear it once in a while, I kind of suspect that might be what it is. I call it "huffing" because it sounds kind of like you when you exhale hard when something annoys you.
I don't think a vet visit is necessary, as long as you take adequate steps like you are.
The tub will help stabilize your temps to a degree, but if the ambient temps still drop too low, you may have to consider a small heater for the room he's in.
And as far as judging you ? Hon I'm delighted to see someone so ready to make necessary changes for the health of their pet for a change! Besides, we all made some pretty dumb mistakes when we got started, I know I did. What makes us good keepers now is that we wanted to learn, and then applied our new knowledge. Sounds to me like you are off to a great start.
Gale