Thailand's domestic flight network is the one mode here that reaches the far south and the north in a single hop, and this page lists 55 bookable routes across 30 starting points. Two of those starting points are both in Bangkok, which is the first thing to settle.
Budget carriers in the region favour secondary airports, and in Bangkok that means Don Mueang rather than Suvarnabhumi. They are separate airports on opposite sides of the city, not terminals of one, so a cheap fare from the wrong one can cost more in transfer time than it saved. Check which airport the ticket names before comparing prices.
Two habits matter more on these airlines than on a full-service carrier. Online check-in is usually mandatory and skipping it is charged at the counter. And bags are weighed — carry-on and personal item both, including when you transfer between airlines, which is exactly where an allowance bought on one leg stops applying.
Island trips are rarely flight-only. Reaching most of them means a flight and then a boat, booked and timed as two separate things.