An AC20 is a decent filter and a good size for your 10g. You could stuff the filter media from the old filter into the new one if it will fit, but I would run them both for about 4-6 weeks if you have room on the tank.
Some bettas can be kept with other fish and some can't, it depends on the attitude of the betta you buy. I would certainly try it but be prepared in case you get a betta that doesn't like tank mates.