Bersa Thunder .380 or Thunder .380CC NIB for less than $300 will give you a servicable weapon with a full waranty. Plus it leaves money for ammo and a holster.
A used S&W 6 series can be had for about $325. They are tough and reliable guns with a better self defense caliber. Get one in 9mm and it will be cheaper to practice with.
If $400 is just for the gun you have a few good choices NIB. I would go with a Ruger SR9c for $390, a Ruger LC9 at $370, a Sig 250 Compact for $375, Sig 2022 for $390, or a Stoeger Cougar Compact for $375. It would depend on which one felt best when I tried them (or held them) side by side.
All of those guns are reliable. Besides the Ruger LC9 they are all compact guns instead of sub-compact guns. I like the added weight and capacity. I really don't find guns in their size range to be hard to conceal. So, I would go with size, barrel length, and capacity over deep cover pocket guns if it was my first CC. They are much more enjoyable to shoot and that means you will practice more.