My vote goes to the .45 acp with hollow points. Get a good one. My wife is tiny and can handle it well. Great one shot stop capability.
.38s and 9mm are easier to handle but have less of a chance of putting an intruder down fast.
.357 and .44s are too powerful for home defense unless you want to shoot your neighbor at the same time.
You discuss calibers, not hand guns. .45 and 9mm are mostly semi-auto. More complicated to operate for new shooters. .357 and .44 mags are mostly revolvers. Much better for less experienced shooters.
.38 and .44 specials in medium sized magnum revolvers are excellent self defense rounds and the larger gun softens recoil. The .357 or .44 mag loads are still an option adding versatility if a person has only one handgun.
My vote: 4" or 6" .357 revolver for overall load selection.
Everyone has an opinion. Some are classy about disagreeing and some aren’t.
If price is an issue, you got pretty much 2 brands to choose from...
Charter arms
Rossi
Both are revolvers as that’s the best for newbies. There are cheaper guns out there but they will be either very scarce, oddball calibers, or questionable quality or all the above(generally).
I would try to steer you towards a stainless revolver of one of the above two brands. A stainless revolver is nice because you can be really lazy on cleaning/oiling/maintaining your firearm without much ill effects. It’s common for a semi auto that sits ignored in a drawer for 15 years to not work when you need it. Not so much for a revolver. Taurus also makes good reliable revolvers at fairly reasonable prices but not as reasonable as the above two brands.
But first thing you need to do is get your wife to a shooting range and rent some guns of various calibers to see what she can handle comfortably.
btw, charter arms has one advantage over rossi...it’s made in america. Unless you know what you are doing, stay away from used charter arms revolvers though. Some years they were making really junky guns.