I just got my medical a couple of months ago and it was pretty simple here in the US. I'm counting weeks to get to the big 5-0. Unless you know there's something wrong already, I don't think you'll have a problem with a 3rd class medical. You just have to find the right AME.
Where would you base your plane? It is true that it's not good for it to just sit for long periods of time. I would want the engine turned over at least once a week, and preferably the plane should actually fly so the engine does more than just turn for a few minutes.
