I would recommend a Hayward sand or DE filter as well. An S160 will hold 100lbs of sand, an S180 will hold 150lbs. Either one is ok. As for DE an EC40 would be most appropriate for that size. I'm not a fan of cartridge, save yourself a headache and avoid one. A 1 horsepower pump is more than sufficient for that size pool. As Kplaster said, a 2-speed is a nice option to save on energy costs if you can get one. They are generally something like a 3/4HP for circulation and a 1 1/2HP for vacuuming combination.
As far as filters go, sand is very cheap and easy to maintain. The sand gets replaced maybe every 5 years. You may find if your pool clouds or is messy at the beginning of the season you will need to help a sand filter out with a clarifier or flocculant. A DE filter will filter much finer size dirt but is generally more expensive to purchase and whenever you backwash you need to replace the lost DE. A DE filter is also a pain to manage when cleaning up a messy pool(it clogs up very quickly due to its high filtering ability).
My personal recommendation is an S180 with a 1HP pump. Hayward's Matrix and Powerflo are the same motor so either one is fine. Hope that helped.