I've actually considered adding a door. The only convenient location would be in the living room and it would still be kinda an odd spot for a door, but I have considered it.
The garage is so small even if I do put stuff on casters, there's nowhere to actually put it. The car almost touches on both ends, and I can barely open the door on either side, so it's a tight fit, but think I'll sacrifice that fact. The thing with having the car in there as well is it makes a mess on the floor, and that moisture seeps through the cement and into the crawlspace below, so I may be better off to make the garage a dedicated shop. So think I'll go with that and forget the basement idea.
If I did do the basement idea though I would seal that area from the rest of the house, so dust/fumes would not be a huge issue. I would not use forced air to heat the area. Maybe just have a long duct run across that room so the heat would just radiate in the room through the ductwork. If I added a duct then I'd have to put a return (assuming the room is sealed) so yeah I'd be sucking up all sorts of crap and spreading it everywhere.