Probably one of the most important things a cello player has to think about is what to sit on while playing. Usually you don’t have a choice and have to take what is available. The best you can hope for is something that does not wobble and has no “arms” to get in the way. (So sadly that comfy lazy boy chair will not work.) It is usually the hardest to fit the young cellists, because they are constantly growing and some children begin when they are quite small. I have found that the IKEA Mammut chairs are a great starter for small children. As they get taller you can add some foam layers to make it taller. I have seen there are fancy chairs specific for musicians that can change height, but I do not know that is really necessary. I would test out a lot of chairs to see which one feels the best.
Ideally you do not want your legs to bend past 90 degrees when you are sitting down on the chair. The feet should be flat and firm on the floor and encourage the student to sit towards the edge of the chair to help with good posture. Try to avoid chairs that have a downward slope towards the middle or the back because this can often cause back aches and have the balance shifted in the wrong direction. You should be able to stand up easily from a sitting position on the chair. (no wiggling!)
Benches can be a great option because this would also keep a player from leaning back into the chair. Players often find piano benches a great fit because they are cushioned, often adjustable, and flat. However, not everyone is lucky enough to have access to one that is adjustable and not susceptible to loud creaks.
I am lucky to have a Wenger chair to sit on which is commonly used in a lot of schools. However, for years I just used a simple folding chair with padding from Target and I would add a cushion to give it some height. Many people I know just use chairs with flat seats from IKEA, or simple dining room chairs.
At the end of the day you have to find a chair that fits you and your cello the best. You do want to try to recreate the same feeling every time you sit down to play your cello. However, unless you carry around your own chair everywhere, you have to be prepared to sit on just about anything.