A 3" K frame .357 may give you sticker shock, especially if you really want adjustable sights - model 66s of this length are well over your budget and there are probably no more than a thousand 3" model 19s. As mentioned above, model 13s and 65s are out there in your price range.
You may want to consider either a 3" model 64 (stainless) or 10 (blue/nickel) in .38 Special; plenty of good, effective SD ammo choices. Finally, you may find an older 2 3/4" Ruger Speed or Security Six, but your best current choice may a 3" SP101, a little lighter and compact than a K frame and you'll probably appreciate the extra mass whenever you touch off a full .357 in it. Good luck in your search.