I'd look for features and then whittle the list down, rather than Brands and Models and hope one fits.
In the price range it's going to be a polymer pistol for an auto, except for the RM380.
Triggers are important, go pull some - the S&W Bodyguard has a notoriously high effort trigger and even had new trigger bars for sale that reduced it at one time. Others aren't nearly as bad - the Kahrs have long enjoyed one of the best triggers out there for a single stack auto and most others are working to get that good.
A slide hold open on the last shot is what duty grade guns have. If you plan to carry it, then practice is important, and having to rack the slide over an inserted mag every time takes the fun out of it. Much less seeing the mag fall out, which is not uncommon. Now, translate that into the problem of trusting that when you really need it - first you get a click to tell you "out of ammo, sorry" then you try to reload pressing against the closed slide, then rack it with very little room for a grip against the mag spring pressure, and you are not guaranteed a clean chambering with no hang up.
Duty grade guns with a slide hold open eject, load, release slide, chamber, fire. Even duty grade battle rifles have a last round hold open, which should be more than enough recommendation to pass over any pocket pistol which doesn't.
How that gun then shoots and reacts to recoil is another amazingly different issue gun to gun. The LCP is considered snappy and there are discussions of it hitting the trigger finger smartly in recoil. Two magazines is plenty and back in the pocket. Shooting the same ammo, the Kahr CW380 is pleasant, and you go thru the box completely.
The magazine reloading also has some emphasis, the Kahr can be done by hand easily going thru a box of ammo with one magazine. My P938 SIG is a bear with mags and requires a reloader if not a bench press to do it.
The cost of those extra mags and if they offer a third finger rest is also something to know. Plus - does your mag offer enough room for an additional round? There are kits that replace the follower (some are plastic from the factory) for a metal one and which have an improved spring, making room for another cartridge. Your 6+1 becomes a 7+1.
Are the sights replaceable? Or just milled lumps on a slick slide? You can upgrade with some guns, others you are just stuck with what you get. Try shooting at dusk with night sights vs none and see which you prefer. Many confrontations are at night, when thugs tend to rise from their lair and venture out looking for prey. That's not overly dramatic - I work retail and it IS what they do. Same reason people carry in Walmart after 10:30pm. I think some employees do, too.
Point being if you don't like the trigger pull, lack of grip, difficulty of reloading, sharp recoil and horrible sights, why even consider a gun regardless of how popular it is or that it's "nearly perfect." Find out for your purposes.
For the most part after a few years the cheap guns tend to move on and pro grade guns that exhibit decent behavior and assist the owner in operation are preferred. And does size matter? Maybe - but shot placement matters more and if you don't practice, the gun is no better than a brand new one out of the box you have never used before. Go shoot it and you will discover if you can really use it.
Buy the features you consider important, be careful of recommendations that suggest one is easier to carry than another and what difference does it make since you won't ever use it?