Advice for research and taking graduate classes for undergraduate student
I am a senior at a large public school in the US, and I believe I can help guide you. To give you some perspective on me: I am part of a program that prepares students for a PhD, and we travel to different graduate schools and talk to the admissions administrators/boards. First thing you should know is that nothing I say is the same for every school, and it is really important for you to look at schools and contact them to see what they desire in an applicant.

For your first question, keep in mind that medical programs are very competitive. To give you an idea, volunteering hours required to get into most schools is incredibly high (varying with 400 hours minimum). You also want a competitive gpa and MCAT, of course. Again, schools will be quite different so take a look at their requirements or contact them.

In regards to research/publishing, the most common thing to do is research in a lab. Both are looked very highly upon (said every school I visited). Since they are both great, then do not ask which to do because the difference to a school is insignificant. It is more about picking which one you enjoy more.

Lastly, are you doing research under an adviser? It is very important to form bonds with professors to learn and eventually receive letters of recommendation. A good way to form these bonds are through independent research under their guidance. You are just starting out so it is important to learn from a well educated researcher and have guide you through your troubles. The advisement is also a form of motivation, because they want to see you do well and you know they will be there for you.

Work hard and be passionate about what you do. Everything is a little easier when you are enjoying it.

Good luck.