You will probably want to work with someone whose goals and expectations are similar to your own. (If not, you will at least want to know what the goals and expectations of the person with whom you are working are!) I'll let you know a little about what I think of student research here. This isn't meant to be an exhaustive list, so please stop by to discuss these ideas with me...
Let's start with this basic statement: Scientific contribution takes many forms. Some contributions offer new ideas. Others implement ideas offered by someone else, often for the purpose of showing how and why they work. Still others bring several existing ideas, either to show how they work together or to unite them within a common -- sometimes novel -- framework.
Generally, an undergraduate research project is primarily an exercise in writing a research document. The project usually requires (1) that the student read on a particular topic or in a particular area of interest and (2) that the student do something, such as writing a program that illustrates an idea. The resulting document describes existing research results, including the student's work, at a level appropriate for a person knowledgeable in the field.
A master's-level project requires the student to do more actual
research than an undergraduate project, but it does not necessarily mean
that the research has to produce novel results. The focus is still on
learning the process of doing and reporting. Often, master's research
reformulates existing work, perhaps by producing:
A good master's thesis should be suitable for submission to a major conference or, if really good, a research journal.
[ By contrast, a doctoral project makes "an original contribution of new and important research results in a recognized field of study." The results reported in a doctoral dissertation are primarily those of the author. Almost all are submitted (eventually) for journal publication. ]
Student and supervisor work closely together. I like to get to know my students, and I hope that my students like to get to know me. As mentioned above, I believe that one-on-one projects provide more of an opportunity for learning than traditional classes do. This learning is often a product of the interaction between student and supervisor, the kind of interaction that is difficult to achieve in most courses.
To be honest, I'm not really interested in supervising a project in which there is nothing more than technical, arm's-length exchange. I'd hope that you expect more out of your research experience, too.
There are only so many hours available in a semester. We all find ourselves constrained by time. As a result, I may not be able to supervise every project that is proposed to me. How do I choose?
First, I have to limit myself to a certain number of students each semester. In order to make the sort of commitment to you that I describe above, I am only able to manage two or three projects at one time. I will try to be sure that I am available for two undergraduate projects each semester.
If I receive more proposals than slots available, I have to select from among them. I generally prefer projects in my own areas of study. Greater preference is given to projects that fit in with or are a part of ongoing projects of my own. This is simply a matter of economics: Such projects will be able to piggy-back upon existing efforts.