There are no wrong answers to filter type. No matter what type you decide, sand, de, cartridge, cartridge/de combo, they all work well. Each has a downside and an upside.
DE filters to the smallest particle, but you have to buy DE, backwash to clean, recharge after each backwash. Once a season, the filter needs to be taken part and cleaned. Grids inside doesn't last forever and need to be replaced occasionally. They clear swamps faster, but in the beginning, you may have to backwash every 15 minutes and you will need to babysit the filter at first. Some jurisdictions do not like DE and require for it be disposed in a certain way.
Cartridge filters are the next smallest particle. You have to hose off the cartridges which can be a pain (cold and wet) at the beginning/end of the season when the outside temps are low. Cartridges don't last forever and need to be replaced occasionally.
Sand filters are pretty simple, nothing to replace, but they take longer to clear a swamp. They are the most economical long term because sand doesn't go bad. Like DE filters, you have to backwash to clean them.
I have a DE filter and I love it. I pay a pool company to clean mine when they close my pool for the season.
Once your pool is clean, you won't necessary notice a difference in any of the filters as they all are great about keeping a clean pool clean. It really boils down to maintenance and cost.