Hi Di
As others have said, best to come and try these areas out for yourself as only you will know which one is "The One" There are loads of rentals you will find, and if you have the chance, test the areas.
However, most of the points you listed as requirements match up to where we have bought - we are in Yambol district - but we are not close to Yambol town, it's about 40 minutes away. Our village is 1 KLM from the nearest town, 15 minutes away from Elhovo town and as such is about an hour and fifteen minutes from the Greece/Turkey border. there is also a nearer crossing to Turkey at Lesovo.
It's a pretty, hilly area (but not mountainous) gorgeous scenery, internet and mobile connections, about an hour from Bourgas and the coast and as in the rest of Bg there are lots of dam lakes and reservoirs here. our house is right next to a large dam lake, so we get a huge variety of wildlife round our way as they all come over to visit the "pub"
I am told we don't get hard winters in this region, but I can't comment on that as our first winter here we spent near Bourgas (where the winter was OK) and our house is an hour further inland.
best of luck, enjoy the adventure.
Karen