The 22/45 is the way to go.The buckmark is the only other currently made 22 that comes close and it is overpriced. I have put a scope on my neos and 22/45 and shot at 100 yards and there is no comparison, plus in my opinion the neos just dont feel right. If you buy a used neos you may have to send it in to get it fixed due to a recall, which I still need to do. The biggest con of the 22/45 is it is a real pain to put back together when you take it down for cleaning.
If I want to go out and shoot I usually take my sig mosquito because it feels like a normal defensive pistol and is just fun to shoot, however they are not terribly reliable. They are just as accurate as a neos but still not on the same page as the buckmark, or the 22/45. (or the old high standards but they are most likely out of your price range too)
edit: BTW the 22/45 and MK II and MK III are the same action with a different grip.