Camping stove fuel type determines cold-weather reliability and travel restrictions more than the stove's design or price does.
The three main fuel types
Canister stoves use pre-filled, pressurized gas canisters (typically a propane/isobutane mix), are simple to use, light, and quick to set up, with minimal maintenance. The tradeoff: performance in cold temperatures can suffer noticeably, since the pressure that pushes gas out of the canister drops as temperature drops, and used canisters aren't refillable, creating ongoing waste and the need to carry spares on longer trips.
Liquid fuel stoves burn white gas or similar liquid fuel from a refillable bottle, and generally perform more reliably in cold weather since liquid fuel isn't as dependent on ambient pressure the way canister gas is. They require priming and more hands-on operation, more maintenance over time, but are refillable and often more fuel-efficient for extended trips.
Wood-burning stoves use collected twigs and small sticks as fuel, meaning no fuel needs to be carried at all — appealing for minimizing pack weight on longer trips. The tradeoff is dependence on finding dry, usable wood, which isn't guaranteed in wet conditions, above the tree line, or in areas with fire restrictions, and cooking is generally slower and less controllable than with a pressurized fuel stove.
Airline travel restrictions apply to fuel, not the stove itself
An empty camping stove itself is generally fine to fly with, but fuel — including canisters, whether full, partially used, or apparently empty, and liquid fuel of any kind — is broadly restricted or banned from both checked and carry-on luggage on commercial flights. Fuel typically needs to be purchased at the destination rather than carried, which is worth planning for ahead of a trip involving flying rather than discovering at airport security.
Boil time and simmer control are a real tradeoff
Stoves optimized for the fastest possible boil time (useful for quickly rehydrating freeze-dried meals) often have less precise flame control for genuine simmering, useful for actually cooking rather than just boiling water. If real cooking, not just boiling water for dehydrated meals, is part of the plan, checking a stove's simmer control specifically is worth doing rather than assuming fast boil time implies good all-around cooking performance.
The one thing people forget
Test a new stove fully at home — including actually lighting it, adjusting the flame, and cooking something — before relying on it for a real trip. A stove that seems straightforward in a product description or video can have quirks in assembly, ignition, or wind sensitivity that are much better discovered at home than at a remote campsite.