It doesn't matter unless you're going to be doing something very hardware-intensive (ex: video editing, substantial photoshoping, audio tracks editing, compiling large multi-object programs, high-end gaming)
You don't say what kind of research you're going to do. If it's reading research or even excel computations for less than 5000 values, then it honestly doesn't matter what kind of computer you get. Just pick the cheapest recent computer ($300-500) at any reputable technology store and you're good to go.
If you want to offer more details about what kind of programs you'll be running for your "research", then maybe I can recommend something else. But right now, I'm guessing just about any recent cheap laptop will do (at least 1GB ram, 1.6Ghz, 512MB cache, though you'll probably find even better stats than that even at a cheap $300-500 range).