To gain entrance into more competitive residencies one needs to first...do well in med school (class rank is key)...do well on Part I of the USMLE (again...key) and be able to interview well (i.e. don't be weird or a jerk). Research is certainly helpful in that it will make you stand out from those who just do well in school. Also, it will give you something to talk about in your interview.
Concerning which types of basic science research are relevant to the surgeon...essentially anything you are interested in is good. The above post offered a good way to learn what some options are. I am a general surgery resident at this time and have completed 2 years of basic science research. I studied the effects of route of nutrition on the mucosal immune system. Other important topics in surgical research at this time have to do with the inflammatory response to injury, modulation of this response, cancer related research (esp. angiogenesis), and vascular biology.
If basic science doesn't interest you then there are always clinical trials, chart reviews and other, more clinical, types of research going on in surgical departments at any med school. If you have further questions feel free to e-mail me.
