The ideal general-purpose service pistol hasn't been created yet. And I doubt anyone will bother. But here goes...
1. Given the considerable female proportion of the forces, and their (on average) smaller hands than men, the gun should be a
single-stack 9x19mm gun with a polymer frame, metal magazines, and a short trigger reach. 10+1 is plenty of shots.
2. Given that handgun training will never be a priority, it needs to have a manual safety and a conspicuous loaded chamber indicator. Yes, those are crutches. But crutches can be handy if you can barely walk.
3. Give it a 4" barrel and enough grip for a full hand to hold it. Polymer frame with a grippy texture and good ergonomic shape, slide and small parts with some sort of Tennifer-esque hostile environment finish.
4. Trigger mechanism... I'd give it a DAO type of trigger mechanism, say a fairly heavy but smooth 8 pound pull, but not a long reach like most DA semi-autos or revolvers. Consistent trigger pull = easier to train to shoot with limited trigger time, and as much as I personally like a 4 pound single-action trigger, I don't think you want Private Joe Marginally Handgun Trained with one.
5. Give it good sights, easy-to-reach and positive controls, and you'd be in business. Obviously it would have to be designed for a very high degree of durability and reliability, but that goes without saying. Give special attention to coming up with an indestructible extractor design, huge ejection port, and maybe even flute the chamber like a Schuemann AET barrel.
OK, enough of my insanity, back to your regularly scheduled gun debate already in progress...