There is no one best kind of filter. Different situations and personal preference will make different kinds of filters better for different people.
Sand
Pros: The simplest to operate, just backwash occasionally. No ongoing expenses except water.
Cons: Lets the largest particles through.
DE
Pros: Filters out smaller particles than any other filter.
Cons: Can require very frequent backwashing if you have algae. Backwashing is more complex than sand.
Cartridge
Pros: No backwashing, the best choice if you have expensive water or water restrictions.
Cons: Cartridges wear out eventually and can be expensive to replace. Some people don't like cleaning cartridges which can be messy.
I add a little DE to my sand filter to get filtering nearly as good as a DE filter without the (minor) hassles of a regular DE filter. Others love cartridges. If you get a large enough cartridge filter you may only need to clean it once a year. On the other hand, you can't beat a DE filter for water clarity. A little of this, a little of that, pick the flavor that you like best.
In all cases getting a filter that is larger than what your system requires will make everything simpler and more efficient.