I'm only a couple of steps further along the road than you are but have an even older Sears lathe, if I get any of this wrong I hope somebody will correct me:
1. Morse Tapers are simply a size and shape definition -- so far as I know, one isn't better than the other, and it's as easy to find parts for MT#2 as MT#1. (I even found a pen mandrel to fit my lathe which is not Morse Taper at all.)
2. Check to see whether the tailstock has a live center, i.e. rotates with the spinning workpiece. (If not, does it have a Morse Taper that can be knocked out and replaced with a live center?) Mine doesn't, and so far I've been unable to figure out how to fit a live center to stop the tail end of the workpiece from burning.
3. Features you could find on a new machine that you won't have on one of these old Craftsman lathes:
- speeds outside the range (both slower and faster) that the motor and pulley arrangement on this lathe give you -- and you'd actually know what the rpm is (my antique lathe has 4 speeds, but I have no idea what they are
- a variable speed motor (saves stopping and moving the drive belt onto a different pulley wheel)
- indexing positions (8 or 12 "stops" to aid in making non-round shapes, eg fluting along the length of a spindle)
There are probably a lot more -- hope this helps,