You can also go to this site
http://www.modelaircraft.org/clubsearch.aspx
and plug in your zip code to get a list of clubs in your area. You could then visit a couple and get more information and make more informed choices.

There is nothing wrong with your original plan either and you can get some beginner electrics in that price range. I'll not advise on that further as I am not knowledgeable in that area however.

Your son is also old enough where he could handle IMO a nitro powered trainer plane if that was desired. The cost to begin would be a little higher but not a great deal and could not be flown in the park you mentioned most likely. You could probably get a nitro plane in the air for about $300 with some frugal shopping.