Miu--I think it's worth the time and money to go to a good running shoe store for a fitting. The height of your arch is just the beginning. They will take a look at the various angles your feet, ankles, knees, etc. make, analyze your walking/running motion, and fit you with a shoe that should help you prevent overuse injury. OTOH, you can just start out and see what happens, then deal with it when it does.
HE--plantar fasciitis isn't a virus. It appears to be an overuse injury. I think the usual treatment is stretching the bottom of the foot, manually flexing the heel and toes.
http://www.emedicine.com/emerg/topic429.htm
(Where are you in the countdown?)
Marta/Five-Leaf