If you have a above ground pool go with the Cartridge or sand, and if underground go sand or D.E. All have their ups and down you should find out what you want from them specifically cause they all do varying amounts of the same thing.
(Filters using literally sand)
For sand filters, on inground pools, I like to use a 30 inch tank diameter, which is a 4.9 sq. ft. filter surface area, and holds 600 lbs of sand. For small pools (under 20,000 gals), I might advise the next size down (24 inch tank), if the budget is tight. But never go smaller than a this for an inground pool.
(like a air filter)
I have a rule of thumb for cartridge pool filters. 100 sq. ft. of filter surface area per 10,000 gals of pool water, as a minimum. I like to see the 400 sq. ft. models on inground pools above 25,000 gals. These can go an entire season without cleaning in most cases.
(Ground up fossilized algae)
Because they offer the most superior type of filtration, people tend to go small with DE, and buy a 24 or 36 sq. ft. DE filter. Ugh - go Big! Nothing below a 48 sq. ft. filter, and if your pool is over 25,000 gals, go with the Big Boy - the 60 sq. ft. filter.
Swimming Pool Blog
Also make sure the filter can take the amount of water that the pump is pushing through it.