What are you running in now? If they work for you, I'd recommend getting the same ones. How much and how often do you run? Have you ever had your gait analyzed?
It's impossible to recommend shoes without knowing precisely how your foot functions and how its shaped. It sounds like you're probably pretty neutral (not a lot of pronation) if you are able to run barefoot on the beach, but not necessarily. If you're serious about running and/or interested, I would highly recommend going to a Fleet Feet or other specialty running store and having them videotape you running on a treadmill so you and they can see exactly what your feet do when you run. Then they can recommend shoes based on that behavior.
But to answer your question of what I run in, I have a high, rigid arch, and am very neutral (I actually think I supinate just a little bit with my left foot). Right now I am wearing the Altra Instinct and Brooks Pure Connect as my daily trainers, Brooks Green Silence as my workout shoe, Saucony Peregrine and New Balance Minimus Trail as my trail shoes, Adidas AdiZero PR as my 5K shoes, and New Balance 1600 as my marathon shoes.