One of the nice surprises I've had is the quality of most of the short scale basses these days. My Epiphone is miles ahead of the old FT-280 that I played in junior high.
Add that to the fact that the lower end of the price spectrum seems to be where the hottest competition is between companies and the results can be quite nice. Am thinking of the Jaguar SS, or Hofner Ignition series or the new Ibanez Talman. Yes, I wish there were more choices (would love to see a modern version of the old Yamaha BB300 series in short scale) but what is there is generally very, very good. And from checking out eBay there appear to be a number of short scale basses that are only available in Japan that might sell here in the US.
As to string choices, it can be all about preference. Personally like the GHS Precision flats on this bass, but wish the E had been .100 rather than .095. Have adjusted technique to make it work just fine. Then again, the only basses I've liked round wound strings on were my short scale Alembic, Rick Turner Electroline and a MIJ Fender Jazz bass where I pulled out the frets and put a few coatings of boat epoxy on the fingerboard.