Let's begin at the beginning--something I imagine a hobbit would say. One of the things that you have to get used to in the Netherlands is how small the kitchen is, and the number of appliances that must fit in into it. In my husband's old apartment, he had to cram a washer, an oven-hob combination, the requisite coffee machine, and a trash can into a space smaller than some desks, and still have a space to put a cutting board. You might not drink coffee and therefore assume that the coffee machine is optional, but it's really not, unless you have no intention of ever making any Dutch friends.
The good news, though, is that stocking a functional kitchen doesn't require that much space. Nor, indeed, does it even require that much equipment. I'd say about 90% of my cooking is done with what's shown below:
The caveat, of course, is that we have a lot of other things in our kitchen. We have several other pots in addition to what you see here, four cutting boards, a small armory of knives, and a bevy of gadgets that are, at the best of times, only semi-useful. But if, at the end of the day, your goal is to put together decent meals for yourself with a bare-bones budget, the equipment shown above is all that you really need. I didn't have much more than this when I lived in Maastricht (I also didn't cook very much, either). The only other kitchen gadget that is a "must" is some method of sharpening your knives--a sharp knife really makes the difference between self-amputation and actually cutting food--whether you go the old-skool way of using a sharpening stone or steel, or get one of those new-fangled things with ceramic discs. But either way, if you're going to enjoy cooking, a sharp knife is a must.
A note on the quality of the items: You don't need to get high-quality cookware, if you're aware of the limitations of cheap cookware. Our pots are staineless steel with a heavy bottom, the cheap-but-not-too-cheap things you can easily get from the Blokker, but I've made do with thin aluminum things before (obviously, tomato sauce was a no-no), and I frequently make stews with enameled pots that cost less than €5 at the thrift store. If you're cooking with thin pans, you need to realize that they don't distribute heat evenly, so what you'll end up with is a scorched circle surrounded by quasi-cooked food if you ignore it for too long. That being said, it's not hard to cook with enameled pots/pans, you just have to get used to it. What kind of cookware you get depends entirely on how good a cook you are, and where your own limits of exasperation and money lie.
The last thing, which is purely optional, but something I would consider essential for eating good food on a budget, is a method of storing food. Most recipes make enough for a family; most food comes in quantities that a single person can't handle. And even if you have a family, there's no guarantee that they'll eat it all. Now, just because you need to store food doesn't mean you have to spend a lot of money to do it: we use glass peanut butter jars, mostly, because they're handy and you never have to worry about them melting in the microwave. If you don't fill them all the way, they're even safe to freeze, and they go directly from the freezer to the microwave without a problem. But I've seen people use old ice cream containers. Creamy salads, which are popular here, come in perfectly-sized containers for storing single meals. If it's got a lid, you can re-use it. There's no need to buy Tupperware.
So, am I missing anything? What would you consider necessary for a well-stocked kitchen?