Water stones (generally Japanese), have much replaced the use of oil stones. Oil stones don't wear as fast generally, and water stones require more maintenance to be kept flat. Water stones of which there are many different brands and grits, give excellent results. You will also need something to flatten them off, and consistent attention to that as you use the stones is very important. Some guys will flatten after every use, and it isn't a bad approach. For sharpening of chisels, knives, and plane irons, using two grits is very standard. I like first using an 800 or 1000 grit and then a 6000 grit. I have stones that go all the way up to 13000, that will give a mirror finish. There are natural mined water stones, but the good ones are extremely expensive, as most mining operations for them have shut down. Synthetic stones have much evolved and are excellent now. There is some debate whether natural stones will give a longer lasting edge or not. Having a proper sharpening set up that can keep your stones in good shape and ready for use, especially if you are particularly working at the same location like your own shop, the stones not just sitting in a bucket if water type, makes things a lot easier. You need to keep flooding them and washing them off as you use them with a tool. I have some oil stones, but rarely use them except for with some turning tools. Like Dave suggested, I've gone through many King brand stones over the years, they work ok too. The course ones wear very fast, there are better. Grits vary somewhat in the ratings depending on manufacturer.
Many folks like the Shapton water stones for sharpening, I haven't tried them. I am currently mostly using Sigma brand stones. Googling either will get you results for purchasing in the US. A good low speed grinder is also helpful for reshaping edges. A well set up sharpening arrangement can't be minimized for getting good results from woodworking tools.