Kitchen knives
You can buy dozens of different types of kitchen knives, and spend a fortune doing it. I have found that Anthony Bourdain's advice (from his famous book "Kitchen Confidential") serves me very well. I have a chef's knife (a large tapered blade, for big cutting and chopping jobs):
and a paring knife (a small tapered blade, for detailed cutting):
...both from the Global brand.
One example of how these two knives can double-team a single cutting job is as follows. I use the chef's knife to cut a bell pepper in half. Then, I use the paring knife to do the separation of the desirable parts of the pepper from the core and seeds.
The two of these will probably cost you about $150 together, but they have served nearly all of my cutting needs. I also sprung for a Global bread knife, once I started baking bread.
I don't favor the long sharpening steels that you see stereotyped chefs using in the movies...mostly because I never really learned how to do it properly. I recently bought a tabletop manual sharpening tool, which you hold down with one hand while pulling a blade through several times with the other (EdgeCraft Chef's Choice manual pocket sharpener):
It works beautifully, and cost me something like $10.
Keep your knives sharp! A blunt knife is, perhaps unintuitively, much more dangerous than a sharp one because it can catch and slip awkwardly. I have the scars to prove it. A sharp knife will also make much easier work in its range of tasks. Case in point, tomatoes are soft inside with a taut skin. If your knife is not sharp, you will smash that tomato as you try to slice it.