If you're interested in doing both, I'd tell you to do boxing first. One, because it will get you in fantastic shape. Despite the fact that you say you're in decent shape, combat sports are a whole different beast. Two, as much as I enjoy boxing, we've all seen what happens when a pure boxer faces a pure grappler, and it is easy to fall back on your grappling skills.
I find that even though I enjoy boxing, I probably don't take it as seriously as I should because I'm aware that I can/will take the fight to the ground, which is where I have the most experience.
If I had to do it over again, I'd start learning to box. Once I had a good start in boxing, I'd learn to grapple. Unless, of course, I could have done them together in which case I probably would have.