I have also done both ways - bought my bike stock and built up my own bike. For price, I agree with everyone that it'll be cheaper to buy a bike with all the components already on - and at the bike shop if you see a bike you like, but maybe they've cheaped out on the front derailleur, ask if they'll switch up for you for a small $$.

Building up a bike is not as easy as it sounds. You have to know every detail of every single component that you want, at the sizes and lengths that you want. Do you know what length stem you'd want? What ratio gearing you'd want? Etc, etc. If so, great and it's fun to pick what groupo set you want. But if you're not sure and don't have much experience, it can be really frustrating and time consuming and really doesn't come out cheaper. And as said above, you need special tools (unless you're planning on having your LBS put it all together for you). The only reason I built up my own bike was b/c I won a new TT frame and fork and so had to do the rest on my own. If I had to choose again, I'd do the same knowing what I know now. But early on in my riding/wrenching experience I would have been really intimidated to build up my own bike not knowing what fits me right or what groupo I'd really be happy with.

But either choice you make, I'm sure you'll be happy with the outcome. Be sure to post pics of your final product! Good luck!