There is no BIFL cheap computer/office chair, a high-end computer/office chair is worth purchasing. After read all computer/office chair requests in /r/buyitforlife, there are going to be four main recommendations, the Herman Miller Aeron/Embody, the Humanscale Freedom, and the Steelcase Leap.
They are all fantastic, they have different advantages and disadvantages that can be hard to describe until you've sat in all four. I personally prefer the Freedom, but my wife swears by her Aeron.
More generally, though, you really just aren't going to be able to get BiFL quality and a good experience out of anything below the $500 range. It looks like a lot of money, but any one of these chairs will be with you for decades, and they will honestly change your life. Remember that you're probably looking at spending eight or more hours a day in this chair and think of the cost annuitized over its lifespan.
Herman Miller Aeron (91 redditors recommended)
Herman Miller Embody (15 redditors recommended)