What are the things to consider while buying a computer chair?

I've spent quite a bit of time and money to decide on this list:

• Get a "task" chair not an "executive" chair, the former has removable arms. Take those off.
• Wheels, and if needed a chair mat, so the thing rolls easily.
• Only need two paddles: up/down and tilt/no-tilt.
• Keep shopping until you find one super comfortable in your price range.

my chair that I have is not adjustable - I don't like it but it is what I could have affordable at that time. So the second thing if you can afford the type you want. My chair has no wheels, I have to push it forth and back - it created some demarcations on the floor. So consider a wheel chair (chair with rollers). My chair has no arms. My arm hangs while moving the mouse - consider it has arms and it should be adjustable too. Also your body size and weight.

@brett_ergosesh probably has some opinions here!