A second-hand laptop will have an operating system. In fact, there would be no simple way for you to test that everything works without one. A laptop running XP or Vista is going to be old enough that if the components are still working, it will be on its last leg (laptops don't have the same physical life expectancy as desktops because everything in them is more delicate). So as a first criterion, I would get one that has Win 7 already loaded.
If you are on a limited budget, you are likely to find that a laptop (appropriately) running Win 7 Pro/64 will be more expensive because it will have a fast processor, 64 bit RAM and probably a lot of it, and a high-capacity hard disk. On one hand, it will be a better investment from the standpoint of being faster, more capable, more easily upgraded, and maybe even higher quality components (unless it is crap hardware on which they loaded a high-end operating system just to sucker buyers). On the other hand, laptops don't have a real long life expectancy, so if it is already used, you are investing in what might be a short remaining life expectancy.
An alternate approach would be to spend as little as possible now to get something to meet your immediate needs with the idea of buying something better when you can afford it and put the cost difference toward the future one. You probably don't need (and wouldn't benefit from) Win 7 Pro unless you are going to be using it to run a network or do software development. The added features in Pro (vs. Home Premium), deal mainly with stuff like group policies that apply only in a network environment. I believe it also comes with an XP kernel, or at least a license for one, to enable you to run XP software in a virtual machine.
If you have a need for Win 7 Pro/64 and are looking for a laptop to load it on, a suitable laptop will already have Win 7/64, either Home Premium or higher. If Home Premium is what is loaded and you need the additional features of Pro, you should be able to upgrade the operating system already on the laptop. You asked an astute question about the cheap online stuff and correctly guessed that the answer is no.
Whatever you get, test it as extensively as possible first. I would seriously consider paying a premium to buy it from a reputable dealer with some form of warranty. That will save you from buying something that fails almost immediately and there is a good chance that the dealer will have tested it.