Eventually perhaps I'll go as far as keeping something in the car (does that require a permit?)
LMAO. You're in Kali. I'd be surprised if it were legal for you to take a piss in the woods without a permit, which you would only be granted after performing an environmental impact study.
So you're looking for home defense and range practice? In those situations you aren't constrained by size so you can get something with decent capacity. G19 is really popular, and used police trade-in G17s can be cheap. Those are 9mm BTW, which is good from a cost perspective and also because your wife should have no issue with the recoil. My preference in self-defense calibers is .45 but it costs a bit more to shoot. The .40sw will definitely get the job done and it's what the majority of police in the US are issued, but the recoil is a bit more snappy. I don't mind but it may not be to your preference and probably not to your wife's either. But those are the 3 common calibers you'll find in semi-auto pistols. For home defense or when size is not an issue I prefer semi-autos over revolvers primarily due to the 2-3x higher capacity. Revolvers have an advantage in simplicity of handling and jam-free operation, but then again I don't rely on a semi-auto unless I've put several hundred failure-free rounds through it anyway. Obviously there are trade-offs that you will have to prioritize for yourself.
My hands are on the slightly larger side of medium. I like .45 so... Glock 21 is 13+1 rounds and the frame is towards the larger end of what fits me. If you have big hands it's no problem, but it's not going to fit most women. They make a small frame version (G21SF) but that one felt awkward to me. If you don't like the lack of manual safety, look at Sigs. In .45 I like the P220 and P220R (railed version). Those are single stack so the frame is a tad smaller than the double-stack G21, and the P220 is 8+1 capacity. Police trade-in Sigs cost about as much as brand new Glocks. Smith & Wesson M&P handles well for me too. There's also the Springfield XD lineup, and the FN pistols are good. I shot all of those before deciding what to buy and to me the G21 had the best combination of features, feel, and accuracy in my hands. There's a lot of personal preference so I can't tell you what to get.
My wife doesn't have any interest in having her own pistol, but if things go bump she is competent to shoot my .38 revolver. If you're starting with one pistol I still say 9mm because your wife should be able to use it too, and even if you decide to go with another caliber later on, it never hurts to keep a trusty 9mm around.
If you're a total noob I'd recommend something like the NRA Basic Pistol course or similar training at a range near you. You'll learn safe handling, fundamental mechanics and they'll get you on paper, usually using .22LR to start off so you're not flinching from recoil.
'85 4Runner (mostly stock) | '94 Miata | '98 Saturn SC2 | '12 Ford Fusion (wife's company car)