A stone basically needs to cut metal off the edge. You should purchase the biggest stones you can afford and have room for. The bigger stones make the job much easier.
The soft Arkansas stones provide the coarser grits, with harder stones providing finer grits. Many people use oil on these stones, theoretically to float the steel particles and keep them from clogging the stone. But one you use oil on your stone, you need to continue using it, or it will clog. If you have not put oil on your Arkansas stone, you will never need to.
Synthetic stones are very hard and won't wear like natural stones. They clean very fast and very well with detergent charged steel wool.
Stones with diamond dust embedded in them cut aggressively. You can remove metal very quickly if you need to, but be careful are you may remove too much to soon. With some diamond stones the diamond dust wears off quickly, leaving you with a useless stone.
Natural stones will eventually wear in the center with use. To flatten them out, mount wet/dry 400 grit sandpaper on a flat surface and rub the stone on it.