I have my own project in a lab and I guess there are a few good/bad things that come along with it. I'm working on a few manuscripts right now, so I have had some experience... here is my say
-more personal time with PI = GOOD. It helps you stand out.
-Gives you the opportunity to be creative. Make ideas, run with them, publish. If you're motivated, there is a lot of opportunity to be successful in a position as open-ended as yours. feel out the lab, feel out the politics, figure out what you can or can't do, in your position, and where you can grow your project, if you catch my slant. If you manage to start building a base of abstracts + pubs (like I did) it's GREAT for applying to scholarsihps, fellowhsips, getting money, winning awards... etc. So basically it's a good opportunity if you figure out how to use it (and this depends on your understanding of the lab and the research itself). This is where the REAL research happens - it's not doing grunt work, it's thinking, analyzing, dreaming, building, discovering, and of course, publishing. But the first five first in importance (significance, meaningfulness, I guess).
-Time. TIME MANAGEMENT IS KEY. Get a lab notebook now. I've been trying to regroup every week not just to write about what I did as a log, but to plan plan plan my projects and experiments. I've spent so many nights in lab past 2am, 3am, it's really taken a toll on my study time, so figure out what you can and can't do, and set goals (lab wise and grades wise and life wise) accordingly. You need to be very structured about how you deal with your time, and how you manage your project. This probably goes for lab relationships as well, being strategic and considerate always.