No one has tried to answer some of your questions, so I will take a swing at it . Hopefully, someone better than me will come along and do better.
As others have said, a multi-speed (step pulley) drive will be all you need for pens, bottle stoppers, tap (as in beer) handles, chisel handles, and lots of fun stuff. Electronically variable speed can be a plus once you get to midi-lathe and becomes desirable as you get to larger throw lathes. Mechanically continuously variable speed (Reeve's drive) can work fine, but the level of maintenance and the shortage of replacement parts for the drive mechanism are generally not a good investment for a new turner.
There are debates about the value of being able to electronically reverse the lathe direction. Some consider it a waste some consider helpful in reducing the amount of tear out when sanding. I tend to be in the latter group for midi and larger lathes.
For my second mini lathe (my first NIB lathe), I could have readily afforded the extra cost of the electronically variable speed, but decided to stick with the multi-speed because there are simply fewer things to go wrong or to be damaged by voltage transients.
On the inspection of a candidate used lathe, there are the simple basics of any power tool: does the motor start and run smoothly (good), are the bearing smooth running (good), does the drive shaft rattle or move longitudinally when wiggled by hand (bad), does the tail stock spindle move in and out smoothly and lock down solidly (good), are the belts and the sheaves in good shape, and are there any cracks or other mechanical damage (bad).
Particular to lathes are:
- whether the ways are flat, level, and parallel (good)
- whether the point of a drive spur exactly lines up with the point of a live center in the tailstock when they are almost touching and the tailstock is locked down (both locks) (good and very important).
Are all the pieces there?
Is there a stand or bench or will you have to build one?
What accessories are included?
Why is the seller selling?
Not part of your question, but also important is a recommendation to check the AAW website to see if there are any woodturning clubs nearby. Often members will be selling there older (to them) lathes as they move up. This can be a good source of quality used lathes that never make it to Craigslist. The clubs often have beginner tutoring of various sorts and they frequently have turning demonstrations as part of club meetings. Our demo this week was on turning trivets (hot mats for the dining table).
Two other key points:
(1) unless you are using carbide tools, you will need a good sharpening system. many of us use 8" slow-speed bench grinders with the Oneway Wolverine system (skip the skew attachment - you do not need it), and
(2) even for pen turning, you want a good quality face shield that the turner is going to wear (always) when turning. many of us use the Bionics shield with the impact-rated face plate.
Welcome to the vortex.
Edited to add the it looks like the Finger Lakes Woodturners are in Rochester
http://www.fingerlakeswoodturners.org/
and they have a shared shop for members with multiple mini-lathes.
AAW lists Kurt Hertzog as the serving president of the Genessee club a bit south of you.