There have been statistical studies of the effectiveness of differing rounds and bullet weights in shootings as to 1-shot stops. (i.e. the perp immediately ceased being a threat after being shot, either incapacitated or dead). The problem is that the sure bets are not always rounds that are easy to shoot (or pleasant).
A bit of judicious searching would probably net you good info.
IMO in your price range, the XDS, slim .45 or the Kahr .45's would be a good bet.
I REALLY like my .45 XDS, but as of this weekend, it has to go back to the company for a recall, something about possible accidental discharge when chamberring a round and/or double firing. Mine works perfectly and is not all that bad for kicking out the SPEER flying ashtrays I shoot. The capacity of 5+1, double action only, but only ALMOST as reliable as a double action revolver. The slide must be racked, chamberred round ejected, the trigger pulled again if it does not go “bang!”.