Firstly, don't make the beginner mistake of saying you're going to compete before you've even walked in the doors. I've been to a few gyms over the past 18 months, and people generally fall into 3 different catagories; those that stick it out, get to an intermediate level and use it as a hobby; those that step up training and eventually go onto fight, and those that flutter off after a few weeks.
The 3rd catagory make up probably 75% of people, 20% make up the first catagory and 5% end up competing. The idea of it fighting is often a lot different to the reality.
See how you like it, how your athleticism holds up and decide if you will compete further down the track.
As for the boxing/kickboxing combo, it really depends on what your goals are. I decided to be a hero and learn all facets of MMA straight away, taking BJJ, boxing, Thai Boxing and wrestling classes.
I ended up overtraining, getting injured and not learning anywhere near as much as I wanted to in each disciplin.
Boxing and kickboxing are actually very different, each coach will pick you up on applying to much of the others technique, and you'll increase the learning curve simply by having to adjust yourself with the fundamentals with each class.
Saying that, they do compliment each other in a freestyle fighting perpective, so if MMA is something you'd like to eventually train, by all means, take both classes.