RE: When to join
One that feels "compelled" and that he has to start jumping through hoops to join the AMA is not ready. If you have no personal assets to risk or are adequately covered by home owners insurance and have a place where they will let you fly you do not need to join the AMA. Should you ever decide to move up in modeling and participate in any organized events you will find very few that do not require AMA membership.
As for safely flying in a 25 acre area, only you can answer that question. Are you good enough to control a model that can transverse the whole distance of the park in less than 20 seconds? I have been flying R/C for well over a half century and I would not feel comfortable in such a confined area with anything more than a light foamy.