Because I look at rubber stamping as a type of printmaking (more on that next week, probably), I tend to use a lot of the same tools I use for other relief printmaking processes. In other words, the same tools I use for linocutting.
My earliest rubber stamps, which I cut from white plastic erasers something like fifteen years ago (back in the days when Staedtler still made erasers in an extra-large size), were cut using an X-acto knife. I didn't really know what I was doing, even though I had done a small amount of linocutting before. They turned out surprisingly well, considering how difficult it is to cut efficiently and neatly with a simple knife. I'll have more on how to cut with different tools a few posts from now, so don't worry if all you have is a knife. It's possible to use one much better than I did back then.
These days, while I still keep my X-acto handy for trimming edges, I do most of my cutting with lino tools. When I cut actual lino, I generally use woodcarving tools rather than the tools sold as lino tools. For not that much more money, you can get a decent set of Japanese wood carving tools that will last a lot longer, and which can be easily sharpened with a stone. I got this set from Lee Valley Tools here in Canada.
They also sell a set with clear acrylic handles that I've heard very good things about, and that I'm tempted to buy as designated stamp cutting tools (I like to keep my tools separate as it cuts down on re-sharpening). I also have a couple of sets of those cheap Speedball lino cutters with replaceable blades that I bought to have as backup when I'm teaching. While they're not that great for actual linocutting -- they dull too quickly and don't re-sharpen as well as real woodcutting tools -- for stamp cutting, they're actually not too bad. Rubber stamp materials aren't nearly as hard as lino, so the tools don't dull as quickly, so once you get them properly sharp, they'll stay that way for a long time.
I do most of my cutting with the small v-gouge, which I find has the best shape for a good, stable cut. The small u-gouge is good if you have a lot of curves to cut (I find the u cuts curves better, though the v is fine, too), but the shape of the cut gives less support to the printing surface. I'll get into that more when I talk about cutting technique, but for now I'll just say that if you only buy a single tool, make it a small v-gouge. Larger tools are good for clearing out large blank areas and cleaning up edges, but the v is best for basic shapes and detail.
If you plan to do a lot of cutting, and get yourself a decent set of tools, you'll probably want to invest in some sharpening tools, too. For frequent use, a strop may be all you need, though it's not something a lot of people aside from woodcarvers have on hand. Lee Valley sells a two-sided strop -- put dressing on one side, and leave the other side clean, and run your tools over it from time to time as you go. Since rubber stamp materials are quite soft, it may be all you ever need if your tools are sharp enough out of the package.
If you're not sure about a strop, or don't think you know how to use one (and they are a little awkward to use on a carving tool when compared to how easy they are to use with a knife), then a fine sharpening stone is your best bet. I have a little stone I got as a gift that has fine on one side and medium on the other, and covers most of my sharpening needs. Chances are, you won't need anything coarser than that for rubber cutting. If you do lino and are hard on your tools, a coarse stone might be a good investment.
Next week, I'm going to backtrack a bit and write what probably should have been the first post in this series: a sort of introduction and my thoughts on the whys and who cares of rubber stamping. The week after, I'll probably begin on technique.