At my teaching studios, I like the nice leather rolling office chairs that are armless. I use the option of rolling around quite a bit when I'm teaching. At home I sit on the sofa. I learned how to play as a kid by sitting cross-legged on the floor in front of my record player.
I have stood up in bands since the 70s; I remember that I had to practice standing up for a while to get the hang of it.
I never really thought about sitting down to perform until I started doing some acoustic listening room type venues. For whatever reasons lots of folks seem to think sitting down and playing "unplugged" (not really, we all know it"s A/E) goes hand in hand. These types of venues always seem to have tall stools. I hate bar stools anyway because my feet don't touch the ground. For performing though, that especially doesn't work because I can't get at my pedals. So when I started working acoustic rooms is when I began including a chair as part of my standard gigging gear.
I have been thrown quite a few curveballs in performance situations with various instruments, so now I make sure I'm covered by checking it out in advance with both standing and sitting. I got a call to do some work several years back with a band that was part Americana/part jam band, and I chose my B-bender tele for those guys. Turned out that the front man had gout really bad, so it was decided that it would be less goofy for the whole band to sit down. Bending didn't work out so well, and that's when I figured out that I needed a shortened strap for seated B-bender playing. The traditional way to play acoustic banjo is to spread the legs wide and just let the instrument hang a bit. When I first started playing mandolin seated, I went with a shortened strap but didn't get on with it. So I wound up using the traditional banjo seated approach for mandolin.
All of the acts that I work with currently stand, except for one duo; my partner still needs to sit after his hip replacement surgery. I will see him tomorrow and I wonder if he has oiled that damn drummer's stool yet like I've been imploring him to do... at gigs the squeak is just annoying, but obviously microphones hear squeaks so you gotta address that with swiveling chairs in the studio.
For traveling, I need a chair that folds compactly and doesn't take up much space. The one I picked has the proper 90¤ angle for my legs so that my lap steel doesn't slide off my legs. Learned that the hard way too. I got mine at Office Depot for about 25 bucks. I need to get something with better padding on the seat though - I'm slender and have a case of the gone ass, A.K.A. snake ass.