I would think about what kind of cycling you want to do long term, get the appropriate style of pedals and shoes, and get used to them. If you start on one type and then switch later on you'll just have to go through the learning process twice.
The main road systems are Look and Shimano SPD-SL. They are similar in design but not compatible. They both give you a very stable platform and efficient power transfer but the cleats protrude from the shoes and make them hard to walk in. Nobody else make the shimano style but there are several cheaper Look knockoffs like Exustar and Nashbar.
Shimano SPD is the most popular mountain/touring/spin class/etc. type pedal. They are nice because the small cleats can be completely recessed into the shoe for easy walking and many pedals are 2 sided so you can always step in without having to flip the pedal. Downsides are that the small cleats can be tricky to lock in and depending on pedal and shoe design not give as much stability or support as road pedals. SPD pedals are made by Shimano and just about everyone else so there are about a billion different designs.
Time, Crank Bros, and Speedplay all make pedals with proprietary cleat systems, but I have never tried them so I will let others point out their pros and cons.
From what you describe of your current riding, the Shimano A520 sounds like the best fit.
Good luck.