Get some professional training.. armed self defense is just another martial art like Tae Kwando or Judo
Until you can sign up for training read this
http://www.saveourguns.com/Ar_Marks_Un_ ... _Guide.pdf
and watch this
https://www.youtube.com/user/FrontSightMovies https://www.google.com/search?q=Youtube ... PQFzdmAO0A
but you need a knowledgeable person watching you shoot and correcting any bad habits before they become bad habits.. giving you tips on how to do it better
LGC here has instructors .. ask if any are near you watch any safety video's like the ones I linked to..set up you phone and record yourself shooting .. compare what you are doing and what the experts are doing in the videos
What you want as far as ammo and accuracy is not necessarily "bullseyes" you want consistency.. you get consistent groups then you try different ammo to see if they give you smaller but still consistent groups
You watch enough video's, some expert or another, will be mentioning what ammo you should buy because that is what they use and that company is who sponsors them .. find a gun forum that has a discussion group of folks that use the same pistol you use and ask what ammo makes them happy .. might even ask on here.. but first.. get consistent understand and accept firearms are just another martial art and is a whole mind body weapon thing and an athletic discipline
I know it sounds like lot.. maybe more than you want to get into.. but to the degree you do make a commitment and put effort into it.. you get better at it
and whenever you get a chance try different pistols in your chosen caliber just one caliber at a time for now.. find a range that rents different makes and models of .380's or a group that will share weapons or let you try their 380's .. everybody is sized and shaped different , different sized hands and every make and model is slightly different in shape and angle and spacing and that can make a difference... finding a pistol that fits you, that naturally "points" in your hand is something only you can do.. every pistol is a compromise .. small 380's designed for everyday carry or concealed carry make more compromises than most because they have to be both small and light with small grips and short distance between the grip and the trigger .. that's not necessarily a bad thing.. every handgun is a collection of compromises and even what is fashionable at the time it was designed.. even a 1911 45 acp has only 8 shots.. but at the time that was 2 more than a 6 shooter way enough even for military combat .. until the "wonder 9's" came along with double stack 15-16 rounds .. 32 acp and 380 was more than enough gun power for gangsters in the 20's, heck some used 25 auto's and 22's and somehow got the job done.. now anything less than a 45 is somehow a wimpy gun according to some
Think of it this way a 380 has about the same energy when it hits the target as Billy the Kid's Colt 45 blackpowder cap and ball give take little on his exact powder load and if he was using round ball or conical bullets ..
But I digress .. every pistol is a compromise lots of room for trade off, one to the other on grip size and how far your finger has to reach to be properly on the trigger among other things .. try as many as you can.. not just hold them .. I mean actually shoot them
But read the book I linked to.. get some professional training or coaching so you get off to good start.. watch the videos to see how the pro's do it do the exercises that you do with an unloaded pistol in the video's work for consistency and proper form not speed and accuracy, that will come in time .. then worry about the ammo.