Tenon vs. mortise seems to be one of those personal preferences topics, and you'll get recommendations for both here on the forum.
Personally, for an 18" rough blank, I would use a 4" tenon in my large chuck. Some folks can get away with a smaller tenon, if it's really well made. If so, I would suggest you keep the tail stock up as long as you can. Maybe that's not feasible on a 20" bed.