There are a variety of camping and hiking stoves. They all work well and your choice should be based on duration of trip and weight for carrying your stove. Altitude plays a minor role.
Over the years the perfection of these stoves have accelerated. They have become lighter, more durable and burn faster. We will address those with our experience and the ones we recommend. It is difficult to break this down to one perfect stove as they all have some pros and some cons.
Gas canister stoves are those stoves that usually have a combination of propane and butane or butane and isobutane. They do have limitations with very cold weather which has to do with pressure diminishing in the tank and cannot expel the gas. Altitude can also effect the stove however many mountaineers still use a canister stove at 20,000 feet. Some of the better brands for mixtures of gas are MSR and Snow Peak. Coleman has failed me a couple times but this had to do with matching up to the stove rather than cold weather.
In the winter I would not advise Primus, Coleman and Optimus. This is due to their mixture of gas and I have routinely had issues when the temps were below 30 degrees F.
Side note: Remember the boiling point decreases the higher the altitude. On average about 2 degrees for every 1000 feet. So normally the boiling point is 212 however at about 700o feet the boiling point for water will be about 198. The boiling point is lower however the cook time then will be longer.
Liquid fuel stoves are stoves that accept a canister. You might be familiar with the red MSR canister that has a hose that connects to the stove. These stoves can take most any fuel, where gas, gasoline, diesel, and kerosine. The benefit is that these work very well in high altitude as well as the cold. No problem working well below zero. The diesel is not as clean and this author prefers the white gas. It would not be much different than having a canister stove. Pros are that it is cheaper, but is still middle cumbersome to pack in and out as the canister stoves are also. They can be slightly more dangerous in terms of combustibility and require more maintenance. If you are not doing a lot of cold temperature camping or mountaineering then stick with the canister stove.
Numerous stoves are on the market for these. Some are MSR, Optimus,and Coleman.
Solid fuel stoves are exactly that. Stoves that are small, lightweight and burn a small solid fuel pellet or pod. One of the most popular ones is the Esbit Stove. It is lightweight but takes much longer to cook on and has low heat.
Great for a cp of coffee but longer for any meal. Great for dried food type meals when you are not in a hurry.
Small canisters that come in various sizes which burn alcohol related fuel. These fuels can be, denatured alcohol, HEET that is carried at most gas stations and even Isopropyl Alcohol. Lightweight but do not put out a ton of heat.