I've used:
A pile on the ground that I put a tarp over
Pallet Collars piled up, which can be made taller as the pile gets bigger.
Daleks
The black skirt things in the picture [next to the green barrel thing]
Pallets lashed together into a box
Tumblers [also in the picture] of many descriptions, bought and home made.
Wormeries, square, round, and home made from old water tanks
In-vessel huge big buggers that turn out fantastic compost at one end, but smell of sick at the other. These cost about £20k though.
Hotbins.
Buried it in troughs.
Surface composted under tarp.
In old dustbins.
I've probably used every design of compost bin that there is on the market, in the various gardens and city farms and community spaces that I've taught or worked in. Plus loads of ways at home and at the allotment.
I've composted in tiny paper pots in wooden boxes to see how easy it is to compost on small scales, through to large Berkeley method composting on the ground which is quick but takes quite alot of energy and space.
And my ones in France now have 8 bits, held together by long poles that are attached to the lid. Which are a right old faff to use.
Plus an old 1 cubic metre builders bag. Which is easy to fill but takes alot of digging out when ready.
It also depends on your space, the effort you want to put into it and
what you are going to use it for. For making potting soil, I'd use a
different method to making compost that you use around trees or use to
mulch the garden with.
In my opinion, the best composting system is the one that costs little or nothing and is recycled, so get whatever you can from freecycle or see if anyone has anything they no longer use that you can get cheaply off them.
The second best method is to get hold of something like the black skirt one below, which lifts really easily off the pile when you are ready to use it or turn it. This really is the best design in my experience.