There are two main types of bar stools - with or without backrests.
There are three mechanisms - fixed, swivel freely and swivel but spring loaded to return to center.
What is your preference? I prefer a backrest for much more comfort and free swivel to make it easy to get in and out of tight spaces.
Kind of depends on how much I drink. Just one? No backrest, fixed. Getting blottoed? Backrest, fixed, so I can turn the barstool 90 degrees and lean either on the backrest or bar, reducing the chances of falling off.
You forgot with or without armrest. I like them with backs, arms and swivels that returns to the center.
This, although you didn’t mention whether cost was an issue, since they would be more expensive IMO.
Back, swivel freely. (I wish my back still did that.)
The ones “where everybody knows my name”. 
Gimme something that looks like I could command an 18th Century warship from it.
The places I hang, they’re tall chairs: yes back, no arms, no swivel.
No option for, “i want a chair that lets my feet reach the floor”? I hate perching on a stool.
This is a throne, not a bar stool. 
As for my preference: my bar hopping days are mostly over, but I have always preferred a solid, non-swiveling stool with four legs and a round seat, no backrest. And yeah, it must have a ring for resting your feet. Like this:
I have a stool rather like a bar stool in my workshop, on which I perch if I need to work on something small and fussy at bench level. It is short enough that my feet rest on the ground (although not everyone’s would, I am 6’ tall), it swivels freely, and has no back or sides. That is the kind I would like at any bar, and I wish I could carry it around with me, because most barstools are very uncomfortable for me. Especially ones with backs, because they are not built for persons with my backside.
Oh, a lot of stools in workshops have wheels for mobility, mine does not. I would hate that.
Sadly long-replaced, but when Bill Nolte opened The Joynt in Eau Claire, Wisconsin in 1973, he obtained the old switchboard operators’ stools no longer needed by the phone company, and one antique barber’s chair at the end of the bar. It made for the most ergonomic drunk in the tri-state area.
Ditto!
If I must sit on a barstool, it has to have a backrest.
You and i can go out to eat together.
Backrest, no arm rests, swivel seat, and a foot rail 6 or 8 inches from the floor running the length of the bar.
Tall seating of any sort, stool or otherwise, must have a footrest at the usual distance below the seat so that one’s feet can be rested easily. Dangling feet sucketh mightily.
Count me with *EinstensHund
Ideally, padded, with a backrest, and a swivel.
But all my local place has are wooden, four-legged stools. Meh, I deal.
The barstools at my kitchen island have tractor seats.
Our barstools in our kitchen and at our wet bar are padded, swivel no back rest. I like that you can just plop down on them from any angle. We play a lot of darts at the wet bar, so you are always getting up and down.
@Beckdawrek , not surprised. That is not an insult. I see the appeal. I’ve spent many an hour on those metal tractor seats. On a tractor.
My wife bought a sign for our house “Farmhouse-ish. All the charm without the farm”