The link I'd bet on is this: Heavy video game users might be more likely to be lower academic achievers than others simply because being a heavy user of anything takes time. If some of the video game playing time takes away from studying time (some of us have a bit of personal experience here...) you have a plausible and easily understood link between video games and achievement -- displacement.
Your proposal (not an experiment, BTW, because ther is no random assignment to groups) instead investigates whether people that are *good at* one thing (video games) are also good at another thing (school). Clearly the game you pick matters a LOT: the more the two things are alike, the better correlation you'll find between them. So, let's say you pick a game that requires the same sorts of skills that school requires. You then find that performance at this game positively predicts academic performance. What have you shown? Two similar things are similar. Alternately, you could pick a game that has nothing to do with school and show that two different things are different.
Here's a crazy suggestion: go to the library. All kinds of research has already been done on video games, with experiments and correlations galore. You might get an idea for a really interesting project by reading about the stuff that have already been done instead of approaching this like the first time someone thought of the question was January 27th at 6:04 am (your post date).
I typed "video game*" into the PsycInfo psychology journal index (courtesy my university library) and I found 157 results, including: "The effect of video games on spatial skills", "The effect of video games on aggression", "Gender differences in video game performance", "A review of research on video games", "Video game playing and delinquency", and yes, "Video game playing and academic performance."
This kind of ask slashdot question makes me grumpy!