Gas versus heat pump
A gas heater is fast and works in any weather, which makes it the choice for a weekend pool you heat on demand. A heat pump moves heat from the air, so it delivers 4 to 6 units of heat per unit of electricity but only when the air is above about 50°F, and it takes a day or two to raise a pool 10 degrees. For a pool you keep warm all season, the heat pump usually costs a third as much to run. Use $1.50 per therm and $0.15 per kWh if you don't know your rates.
Keeping it warm
Heating up is the small part. An uncovered pool loses 3 to 5°F overnight, mostly to evaporation, so maintaining temperature costs roughly this much again every few days. A solar cover cuts evaporation by 90% and is the best return on money in pool heating. Under a cover, a heat pump often keeps a pool at 82°F for $100 to $200 a month.
Sizing a heater
Heater output is rated in BTU per hour. Divide the BTU figure above by the hours you're willing to wait: 1.2 million BTU over 24 hours needs a 50,000 BTU/h heater, over 6 hours a 200,000 BTU/h one. Hot tubs heat fast because the volume is tiny; see the hot tub calculator.