If you're interested in a revolver, a .357 magnum is a very versatile and proven choice. Can shoot several different rounds (true .357, .38 specials and IIRC a couple other less common) with everything from a high powered load to a varmint round. Lots of women I know (mother, sister, a couple girlfriends) are/have been fans of the .357 due to being a good size with decent power.
Also, revolvers are a lot simpler and more reliable -- at least for folks who are only occasional users. Pistols and semi/auto rifles (even most of the really expensive ones) require diligent care to remain reliable whereas a half decent revolver just needs very basic attention. There's a reason cops/marines/etc. have a TV trope of always being shown cleaning and oiling their pistols.
You can either get an "old fashioned" double/single action (i.e. one with a hammer that you can cock manually or not) or some newer designs that have no (external) hammer and are double action only. Taurus (and others probably) make a whole lineup of revolvers like that. The benefit of the Taurus types is more simplicity and quicker action.
There's also small and large frame options. Typically the small frame options are better for people with smaller hands but only have a 5 round capacity while the large frame models have a 6 round capacity. You can also get models with swappable barrels (I have a 2", a 4" and a 6" for mine) for different scenarios (something you can't do with anything but specialty pistols) though that's probably out of your stated price range.
If you're interested in a pistol instead, well you've got some research to do as the available styles are practically innumerable (actions, materials & construction, striker/hammer fired, safety mechanisms, center/rim fire, grip style, etc.). The best advice I have is to check around for a local range that will let you rent/try before you by and try out lots of different types before you buy.