Regarding buying cycling shoes online, I don't see the harm, just make sure the online place you buy from has a return policy. Remember the cleats usually come with the pedals, not with the shoes.

FWIW, I have been using mountain shoes with SPD cleats/pedals for years now. I started using them for spinning indoors, and found them much stiffer than regular running, cross training, or tennis shoes. This results in more efficient pedaling and less foot fatigue during longer rides. After using them for a time on the spin bike, I bought a set of SPD pedals for my hybrid, now use them on my road bike.

I am sure there is some advantage to road shoes (lighter, even more stiff?), but the downside is, you can't really walk in those shoes, whereas you can in mountain shoes, which have a recessed cleat. If there is any chance you will get off your bike and need to walk more than 100 feet, mountain shoes work much better in the real world. The alternative is to plan to bring a change of shoes along with you on the ride, which strikes me as an unnecessary hassle.