While there are many different kinds of what we might consider true camping chairs – those built to be packed up and carried into the wild on your back – the prototypical classic camping chair is a three legged stool. Regardless if they have three or four legs, minimalist camping chairs should be lightweight. The idea is to have something to keep you from sitting on the ground and help to keep your fanny higher than your feet. These camping chairs do tend to favor function over comfort despite the efforts of some manufacturers to find new, novel solutions. I have used a simply kind of chair like this for many years. I also have another kind of simple chair in my car for more than twenty years (the same one!). There are two important things to consider if you are looking for a simple camping chair.
The first important consideration is weight. Are you are taking this chair on a backpacking trip or if it will mainly be carried around in your car? The chair in my car is four legged and made of wood. It is like an accordion, folding into a flat form via a hinge about half way up the legs. When I unfold it the legs separate, forming a solid four point base. The seat is a piece of canvas and it is held between two pieces of wood at the top of the frame. When the chair is opened, the wood supports holding the canvas separate and the canvas is pulled tight.
It is not hard to make a relatively cheap but good seat if it has no bells and whistles (armrests, back, cup holders, etc.). I included all these details to make the point that a good simple chair is a solid chair. The canvas, wooden construction and the way it can plant itself on the ground makes for a safe seat. It is not good for putting in a backpack. To bulky and its weight make it too unwieldy for a long back country trip.
The camp supplies industry has therefore taken the idea of a simple stool and tried to make folding camping chairs that have a strong focus on light weight and minimum bulk. The problem with this is the poorest built of these are worthless. They either have a tiny little seat (which is fine if you are skinny and have a tiny a$$!) or they have a poor support system. The small seat problem means instead of being supported you will be uncomfortable as parts of the chair will literally be poking you in the butt. The support system problem is another issue. Spindly legs are usually not the primary culprit except in the case of some really badly built (usually super cheap) models. The issue is one of design flaws: either the chair itself is not well balanced or there are not good feet. In both cases there will not be a solid base formed when you sit down and pressure is applied to the seat. I once had a chair like this and quickly got rid of it. It was not worth trying to sit in a camp chair where I had to be careful not to tip over.
So what is a good chair? I should say that I can provide some recommendations based on my experience, but not necessarily based on having used the models I provide links too. My wooden carry-in-my-car model is a no brand cheap model I picked up at a large recreation/outdoors store. I can find what I believe is an equivalent, and here it is. This one is actually metal and canvas. Some reviews say people have taken this model camping but it is a bit of a pain due to its size.
As for other backpack type chairs, most of the more hi-tech/lightweight manufactured goods for camping are constantly evolving. The last backpacking type chair of this kind that I bought just a few years ago has been replaced by newer designs. I can tell at least point out that something like this (cheap and it shows!) is to be avoided, while this (low priced) and this three legged chair (an expensive Cadillac model: well built, lightweight, comfortable) look to be solid models that I would buy.