I don't have any personal experience living in any of those villages and, if it's a large and 'rambly' one (like Sha Kok Mei and Hing Keng Shek), the actual house and/or part of the village can make a difference. I think, unless others have personal experience in these villages and can check it out for you, you'll probably need to see the place yourself for any of these in order to cross any off or prioritize.
As Skyhook says - the Country Park (that's Sai Kung Country Park - Pak Tam is the main road through it) is a good possibility for you considering your budget and space requirement. There aren't many available at the moment, though, as far as I've heard.
Best of luck to you - it's not an easy task you have ahead. Pop into our shop when you get into town and we'll give you lots of tips on where to find things, best places for.....etc. We've become the de facto "SK Info Centre/Community Advice Bureau"
Judy at Explore Sai Kung