Three things:
1) Tazer. Mark is right about the middle aged thing. It might be an interesting take to have them allowed to use lethal force on people of a certain age but not nonlethal because the non-lethal might kill them.
Also, they porbably would have a low-grade stunner for the same purpose.
2) Sidearms. I'd go with the Beretta Commando or a similar gun. It's the setting equivalent of the 9mm. the ranges might seem like an issue, but from an in-game pov they really aren't an issue. Something like 90% of modern gunfights occur at less than 25 feet. If a person if farther away than that, they are probably running from you on a public city street any your gun should not be firing to begin with. This is almost exactly the medium range of the pistol, so I see that being the standard in most places.
3) Shot gun. What most people don't realize is that the shot gun's main purpose is deterrence. There's a reason why law enforcement still uses hopelessly outdated pump shotguns. Whenever they upgrade to semi-auto, they have to kill a LOT more people. The reason is the sound of a shot-gun pumping has a staggering psychological effect. In some law enforcement, it's considered the equivalent of shouting a warning. So I think they middle of the console weapon would be a plasma carbine, but not just any plasma carbine. It would be a weapon that make one hell of a whine when you flip off the safety, and that whine would strike terror in the hearts of any criminal who watches the futuristic equivalent of television.
4) Androids are only expensive when you buy them. Once they own themselves, they are probably less expensive than biological employees (for a variety of reasons. No secretions adding to the wear of chair upholstery, for instance). Having a naval droid that's bought off its initial bill and left the navy would be an interesting choice, as would a pleasure droid that's joined the vice squad.