LCP or J-Frame?
I concur with those who said that the decision as to what you carry is a personal choice which is so specific to you and your particular needs, no one can really decide that for you. With that said, I will give you some of my opinion and insight on the matter.
My EDC is usually a Glock 29 (10mm), rarely but occasionally substituted with a G-23 or G-27 (.40's). Along with these primary carry guns, I always have at least two magazines of spare ammo on the belt. My favorite carry mode for all of them is a pancake style holster on strong side at about 4:00. I am a retired cop and for a while, only carried the primary and the extra mags. I now also carry a LCP in a Fobus kydex holster at 11:00 in cross draw mode. The LCP is loaded with 95 grain T-Series and I carry no additional ammo for it on my person, although there is usually at least an extra fifty or more rounds in the car, as is the case for other calibers.
A few years ago, in a nearby city, a heinous armed robbery and murder occurred which was unprecedented in this area. Sometime after 8:00 AM, a lady was at the drive-thru ATM at a local bank in her mini-van. There was a line of cars behind her and employees of the bank were getting ready to open on the inside, with some looking out at the drive-thru and ATM area. A male subject walked up to her driver's side window and pulled a handgun and shot the lady several times through the open window, killing her. He dragged her body from the van and onto the ground, got in and drove the van away. He was later apprehended and it later came to light that he had been riding around with other cruds who were helping him, "find somebody to rob", that morning.
People who know I am a proponent of CWP asked if she would have survived had she been armed. I had no good answer for them. When I read of such cases, I often try and mentally put myself in the place of the victims and critique what the victim did, what I would or wouldn't have done differently, and what outcome I would have expected had it been me in the victim's place.
In this case, I didn't know. Would I have mistaken the approaching perp for a (usually harmless, though annoying) homeless person or panhandler; or would that sixth sense we all have and should learn to heed have been on high alert and would I have the G-29 leveled on him as he approached my window? I just didn't know. This was the catalyst for my carry of the LCP. I purchased the LCP about four years ago with the idea of using it as a BUG for those nights when you have that nagging feeling of foreboding and nastiness which we all get from time to time but which thankfully only rarely come to fruition. At that time, my department did not sanction backup guns so this was a frivolity of sorts. Thankfully for the guys who still work there, they do now sanction BUG's.
The LCP has been a reliable, very accurate, little gun for me. I have little trouble keeping all seven rounds in the torso of a standard silhouette target at 25 yds with it. Even so, I have never been able to make myself carry "just" the LCP. It always rides along as second fiddle to something larger and more powerful.
My reasoning in carrying it in cross draw mode as backup to bigger and better things was that from a sitting position in a car, I would have to telegraph too much, much too soon, to an approaching perp. Had I been in the murdered woman's seat and not realized what was fixing to happen until late in the game, I would have been dead meat, drawing from under my shirt on my strong side hip. Same if sitting in a local Waffle House at 3AM, which I do on occasion, when the place is being robbed. Drawing from a cross draw from under my un-tucked shirt can be accomplished with far less unnecessary telegraphy to the potential assailant. If faced with such an unenviable situation, my hope is to make a head shot(s). Yes, I practice head shots with this gun when I shoot it and can do so comfortably out to seven yards.
Sorry for the digression. If forced to choose between only an LCP or only a J-frame .38, I would definitely go with the J-frame. I can't help but worry that the perp I might run up against would be on the heavy side and the .380's might not go deep enough to cease hostilities. Double; no, TRIPLE that if the perp happens to be a "duster" or is otherwise de-sensed to pain and normal incapacitating influences. If you can handle the recoil, carry some good +P ammo for the J, if that is what you decide to go with.
Whatever you decide, I wish you good luck and hope that for you, as well as myself, we never have to drop the hammer on anyone but if we do, we come out of the ordeal still in one piece.