If your park is big enough and there is not much activity and flying your plane is not forbidden there, then it's fine to fly a small electric.
And the fence line to a neighboring property is not too much of a problem, since the airspace above it is not part of it.
Make sure you are high enough and don't disturb anyone. If you fly your helicopter in someone's backyard and ruin some old Lady's hairdo, you might be in trouble...
Flying a nitro or gas plane is not ok in most parks. There are just too noisy. Keep in mind - all it takes is a few complaints and there will be some new regulations and you are done flying there.
Membership with the AMA is not mandatory, but it is a good idea to have some insurance. It's a good reason to join.
I think park flying is a good thing, you might get some people there hooked on RC flying this way.