In 380, I have been pleased with the Bersa Thunder/Firestorm .380.
Reliable, and the trigger pull is not horrendously heavy in either DA or SA mode.
Others have made good suggestions there also.
If this is home defense, does she want a weapon light? or will she train to use a flashlight?
I would figure that out, and then decide if it HAS to be new, or if a good condition used one will be acceptable.
With those two pieces of information, you can really start to narrow down the suggestions.
Lastly, how familiar with handguns is she?
If it were my daughter or son, neither of whom would hit the range more than 2 times a year if I forced the issue, I'd probably guide them toward a reliable revolver. That way no worries about training for clearance drills.
For inside the house, I would use .38Sp+P rounds, as .357 would be more likely to go through the apartment wall and the sonic crack is more damaging to ears at 3 am when someone breaks in.
$250 is a real difficult price point for fans to recommend.
You are asking for it all- quality, at rock bottom price.
I am going to throw a curve at you: See if you can check out the FMK 9C1 G2 pistol.
I am in California. I have more handguns than I need, but not as many as I want.
If I lived out of california, i'd be REALLY tempted to get their single action pistol.
I have dry-fired the DAO pistol [CA Approved], and found the trigger reset longer than I liked [more like DAO revolver- by design].
I was impressed with the way it pointed and fit my hand. Never shot one.
I seem to recall seeing them for low $300s, and they have 10-14 round magazines, with a picatinny light rail. [and come in colors! ].
Just a thought.
It isn't a Glock, or M&P, or Xd, and it is cheaper than any of them new.