I bought this a few years ago and have been pretty happy with it: [https://www.amazon.com/dp/B00IKBL2ZS/ref=cm_sw_r_cp_apa_i_3rT6CbHY8H8QF].
It's over your budget, but as others have stated, it's risky to go cheap on a work chair you plan to use for hours at a time.
Another option if you're not looking specifically for an office style desk chair might be an upholstered Parsons dining chair or similar. They're nice and cushy, and you can find fairly basic ones at reasonable prices on Amazon, Wayfair, and sometimes at thrift and second hand stores.
Drum thrones make awesome guitar stools. It costs a bit for a quality one, but your ass will thank you. Alternatively, look around for office chairs without arms. This is what I have in my room and I love it. The leather feels very high quality, for the price, and it's been very sturdy so far.
Boss White Leather armless I also have a chair pad I've used for years as well that I put on top of it. It's comfortable to me.
Although the chairs in my college library are stupid comfortable but they cost $400 a piece. I might end up buying one some day.