Running new power to above ground pool

You can run direct bury romex, for that run I would use 10/2 with a ground.
Typical 20Amp circuit is 12/2 romex you might get away with 12/2 but above ground pool pumps are 110volt and pull large amps like in the 15 amp range.
You might want to run 12/3 and see if your pump will run on 220 about 4 amp draw.
By the way 12 = 12 gauge and the 2 = 2 wires.
You will also need to install a 20 amp GFCI Breaker, or get an outdoor GFI plug and box.

DO NOT RUN extension cords as you will burn up your pump.

I heard through an electrician I talked to after I had my pool installed that 220 is the better way to go as far as cost and wear and tear on your electric motor in the long run its better.

The advice you received regarding the cable is absolutely incorrect.

First off, Romex is never allowed to be buried. It cannot be in any wet location. Let alone in the ground.

There is a cable that looks like Romex, but is it called UF cable, and is allowed to be buried,

However,

UF cable is not allowed to be used for pool wiring either.

Most locations allow widely used Sch 40 PVC conduit, complete with all fittings , and pulled through THHN/THWN or XHHW wire.

Pool wiring is very critical. Best to contact your local electrical inspector. Each state and city can have their own specific requirements for pools, along with the National Electric Code.Many will have a detailed sketch showing exactly what is expected.

Use 240 volt rated motors if available. They don't run any more efficient, but the higher voltage will help with the voltage drop. The distance you have will require voltage calculations to be done, based on the voltage, HP of the motor, type of wire used, etc. Guessing here does not work.

I am the first to help a DIY'er, but with pools, there are many various requirements all changing with the wide differences of the situation.

Ground fault breakers, special grounding, locations of outlets and lighting, only to name a few.

Best to call in a pro on this.

I am installing a above ground pool about 250ft from my house, I know there is a voltage drop,motor is 115v and 12 amps, what size wire and gfci breaker should I use.

For the data provided , this motor will need #6 copper.

Better of using a 240 volt motor, same size would need #12 wire.

So, your saying 240 volt motor use #12 wire and 2 pole 20 amp gfci breaker. And at the motor I will have 240volts ?

Yes, but the motor will need to be rated and connected for 240 volts.

This assumes the motor will be 6 amps at 240 volts.

A 2 pole 240 Volt GFI circuit breaker will be needed.

I just got done doing this same thing, and the variance in code is crazy from town to town. I ran a new service cable 4-4 from the main panel to my shed where I installed a 100 amp sub panel (180 feet). Also be careful, our local home depot told me 18 inches buried was satisfactory where in reality I had to go 36 inches (rented trench digger for this $114 for the day). I then ran 12-3 UF in conduit from the shed sub panel to the pool power post (40ft). All cables had to have 5 ft of conduit going into/out of the ground. I did all the work, had an electrician verify and sign off my permit ($86) and make my connections. Inspector was thrilled and I am all done. All in all, about $700, service cable is not cheap.

If you use 240v instead of 120v it will cut the amount of amps the motor pulls in half, which in turn will lower your electric bill. I do not believe you need #6 for a 240' run. Voltage drop does not play much of a factor until you pass 300'.