I have more .380s than you can shake a stick at. Some sort of sickness.
I have both the Keltec .P3AT and the Ruger LCP.
Same gun, basically. The KT is rougher, which you may prefer for grip. the Ruger is more polished but also more slippery.
Either will come out and go bang reliably. If all you want is a double-action pocket pistol, you can stop reading now and go shopping.
Buy the pinky extension for at least one of the mags. Makes a big difference in comfort and control.
More expensive choices include the NAA for about $400 and the Rohrbach. Both are all-metal, a bit fatter, and blowback.
I've not shot either as they don't particularly interest me. I like slim guns with locked breeches.
My favorites are the slighty larger mini-1911s.
The only one in current production is the Sig P238, which is a direct licensed copy of the old Colt Mustang.
This is all-metal, with a 1911-style safety. Actually, it's a better safety, as you can set the safety with the hammer down, so it can't be cocked, and the slide can't move. Further, the safety actually moves the sear away from the hammer and trigger, which the 1911 does not. Just now being produced, about $450 - $600. It's a little fatter than the KT or Ruger, but it's heirloom-quality.
If you want a nice, new pocket .380, and don't mind it being slightly bigger and heavier, go look at this one if you can find it.
Older designs well worth looking at:
Colt .380s - Mustang, Mustang +2, government - all are mini-1911s, $500 - $800 used.
Star S, SS, DK etc - Excellent small pistols. The S or SS is slightly larger, but very slim. High quality. Colt copied the Star design for their .380s. $200 - $300 used.
FI Model D - Also a Star product, and the original colt Pony. Very-pocket-size, very high quality, hard to find, $350
Llama - Look for the very early or very late versions with no rib on the slide. The small-frame Llamas made before 1950 are very high quality. They are the most "to scale' miniature 1911s I have found.
All of the above are fixed breech and a pleasure to shoot.