I don't really have any handguns that are "beater" guns
All I can do is tell you what
I would do in your shoes then.
I would hook up a family member with a CZ82, a brick of ammo, and range time ... or help them get their own guns.
The exact gun might change over time, but the CZ82 is (in my opinion) the current best cheap surplus gun, it runs pretty damn well, fires a viable duty caliber cartridge and has 12+1 capacity, as well as being easy to operate.
And I wouldn't care if they carried it without a permit, either ...
not my problem ... I would encourage them to get a permit ASAP, but adults can break the law on their own, I really don't care.
I would still balk at introducing a firearm into the home of a prohibited person, though. Case-by-case evaluation would be required and I might distance myself further if the GF is prohibited for a silly reason and I'd avoid the whole situation if she was prohibited for a reason I agree with or was just plain non-responsible.