Same - the LCP was enlightening compared to a Glock 19 as a CCW gun. I couldn't then but MO finally offering permits changed things up. The first gen LCP had a somewhat notoriously difficult trigger, while the new ones are reportedly better, but it's got a snappy recoil that some don't like.
Both those features left be cold, although carry was very easy in a pocket holster. I sold it and moved back to a compact, but they are just a tad too big for easy concealed pocket carry.
I recently started looking again, as a P938 isn't pocket carry for me. I read reviews on line, with the idea that testers and bloggers sometimes get carried away with a new gun introduction. I also read owner comments on forums, and in the search ran across what features I considered to be optimal.
First, weight - the lighter end of the scale is near 10 oz. At this weight most are within fractions of an inch of each other. Then, trigger pull, which was the number one reason I sold the early LCP. Most pocket guns are some form of Double Action Only - you have a long trigger pull at a weight above 6 pounds. Trigger pull to me is important as my older hands suffer a bit from abuse over the years, plus you can only pull back on a trigger so far. If the gun has a short length of pull then the trigger finger curls so far back only someone with stubs can operate it. In most of the cases I would be better off cutting my finger down one joint and the gun would fit perfectly. Not happening, so triggers that required pulling completely back to contact distance with the frame were out.
Next are other features - being largely DAO no other safety is offered. A slide lock is next, some actually hold back the slide on the last round, others only offer some form of disassembly, and they can be rude about it. Some too hard, others far too easy. I chose a gun with a slide hold open, which also is how it's chambered, same as it's bigger brothers and a lot of duty guns, which I am familiar. With a slide hold open, it locks back on the last round - telling you that you are out of ammo, not deceiving you to wait until the gun goes click on an empty chamber. Holding the slide open also compensates for a stiffer recoil spring - you only have to rack it back once, after that you swap mags and drop the slide, to shoot again. With non hold open pistols you might load against a closed slide, which adds spring pressure to the force needed to seat it, and then rack the slide against that pressure which adds to the overall force. And you have to do it every time you load. Not for me.
There are some guns with magazine disconnects which prevent you from firing with just one round in the gun, they are supposedly a safety feature. I've shot larger guns with them and without, I haven't found the complication necessary. There is a circumstance where in the holster or when grappling with someone the magazine button could be depressed, rendering the gun unusable. Some say that is good, others a disaster. For lack of a better viewpoint I consider that a draw and it's unlikely anyway.
I haven't seen any of these with a drop hammer or other lever, but it does go to second strike capability. Getting another hit on the primer with a second pull on the trigger is considered a good thing, most testers found they would go off the second time. That feature is common with hammer guns, but not striker fired ones. Those ignition systems are quite different, and it also goes to how much the mechanism is prestaged, which is commonly done at a "half cock," and the trigger then completes the action finally releasing the force. It's also directly related to the weight and length of trigger pull, and you can have too much of both. In my case I chose the shortest lightest one I found both reading specs, owner reviews, and sampling in stores.
I bought a pocket pistol, made in the USA (important to some,) weighing 10 oz unloaded, polymer framed, which gets the price in the low $300 range. It has a six pound trigger, which is one the low end if not the lowest, compared to the M&P BG380 at 12. ( but I recently heard of a newer versions lighter weight.) LCP's and most of the rest seem to run 8 to 10. Trigger pull length was shorter than the LCP or RM380 - I had to pull back on that so far it touched the frame on release. Far too long for me. And the gun had a slide hold open, which I feel speeds reloading considerably while eliminating the mag dropping out or racking the slide every time.
Do your work, just settling for the first one at a cheap price might work - or might not. I didn't for me, and a lot of the auctions and sale forums point that out. Like a larger one, specify what you want and then decide in the face of the limited offerings what to compromise on. I would likely be happier with a SIG P238, single action with safety, just like the P938 I have, but the little .380 is near 15 oz empty. Instead I chose the 10 oz one with the best DAO trigger pull there was. A Kahr CW380. I chose it because it was the better tool that fit the job, not because of a cheap price or I thought it looked cool, of which there is an abundance of in this market. I know it's the bullet that does the work, I just needed a good applicator.
It's in my pocket where no one can see it, what it looks like means nothing.