There are differences of opinion regarding what you are asking here. Some people are insistent that a road bike has to have proper road pedals, others think that for non-competitive riding over short distances the mountain bike style pedal is just fine, so long as you don't go all day in them and expect to win the Tour de France in them.
Let's look at the difference in shoes first. Road shoes have a huge cleat on the bottom of them that makes them not suitable for walking in off the bike. Meanwhile, mountain bike cleats are embedded in the sole and you can walk all day in shoes with them, just so long as you avoid polished wood floors that don't need to be scratched.
Cycling shoes have an upper and a sole. If you look at the market leading Sidi shoes the same uppers are available on both the mountain and the road versions. The soles are also remarkably similar, or at least the upper part of the sole. They have different rubber attached to the sole and different holes in them for the respective cleats.
Because of the different soles, with more rubber on the mountain variant, the best option for town riding is to get the mountain shoe. This is because you can ride them quite easily without being fully clipped in. With road soles this is not so easy to do, particularly in the wet, as you have to clip in properly before putting in any power strokes to get across that junction. They are also one-sided so you need to be adept to get into them. By contrast, you don't have to clip in with mountain bike pedals at all (if using Time Atac) and the cleat is always there for you as they have the cleat on both sides.
For where you are now, consider getting the mountain shoes, they have the same uppers and stiffness to the sole, if you pay for it (e.g. Sidi). You can also get more pliant shoes such as the Shimano affordable models that are stiff but not super-stiff. These can also be more presentable off-bike.
Remember that whatever pedal system you use the pedal, big or small still attaches to the same size hole in the chainset. Shoe stiffness with glass fibre or carbon fibre is huge so the platform size is not the be-all-and-end-all.
There is another choice to be made with the actual pedals. Shimano are the market leader with their SPD system, this has been earned not because it is a better pedal system. The other pedal system to look at is the Time 'Atac' range. This uses a smarter spring system that allows your feet to 'float' a lot more naturally. The 'Atac' pedal system is patent protected, the designer was the guy that designed the original road 'Look' pedal cleat system and I think it has a lot more going for it than the clunkier Shimano efforts.
Have a good look online for opinions regarding pedal choice/reliability and remember that most people defend their pedal system choice less than objectively. Generally shops will only stock the Shimano pedals or the 'Crank Bros' pedals and people that buy these will swear they have the best system.