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This may sound a bit generic, but aside from selecting a preferred caliber or selecting the manufacturer that you trust, one of the most important things about selecting a pistol is how it fits in your hand.
The bigger your hands, the wider range of pistols you can comfortably enjoy. Secondly, if you are going to carry this pistol legally concealed, you're going to want to consider one that is slim and fits your wardrobe/body/type of clothes you wear every day (I use an in waist band (IWB) kydex/leather holster and carry a slim single stack 9mm). Some people, don;t ever wear clothes that would make an IWB holster realistic (like women who like to wear stretchy pants and stuff). In that case you want to pick something else like a shoulder holster or something that is comfortable (be careful with "bands" like belly bands unless you are fond of having your pistol fall out when you are walking through town)
Springfield makes reliable, high quality pistols. I have a Springfield XD45 that holds 13+1 of 45ACP. This is all fine and good but when the magazine is full this pistol is heavy. It is also bulky, so if you don't mind stuffing something big and bulky in your pants for the whole day, or if you pick a shoulder holster or whatever, fine. I use the XD for carrying OWB holstered, unconcealed, when I am roaming around on my land/hunting/whatever because then it's not really a weight/bulk issue for me, I am 6.0" 220lb or so.
380 is OK but if you can comfortably carry a 9mm you may want to go that route to get a little extra, the 9mm typically is about 150fps faster and penetrates a little more, like 11.5 inches in gel vs 10.5 inches for the 380 for example. Also 9mm is super-common and gives you a little more flexibility when shopping for ammo. But I'm not going to bash on the 380, my wife carries one and is comfortable with it.
last, if you can get to a range with the pistol you like, or one very similiar in weight/mfr/mechanism, see if you are OK with the recoil and the way it behaves. You can take the big XD45 and smoothly shoot at a target without much recoil management because it's heavy and doesn't have a lot of muzzle jump. But if you take a little Ruger LCP 380 that little guy has some good muzzle flip and you need to be aware of this. Light pistols are nice but then you have to pay the price in recoil and flip (and often a shorter barrel length - which will give you a little less accuracy, more muzzle blast and a little less FPS than a longer barrel).
Get your hands on a few if any way possible- borrow from friend at a range or what have you - be safe and always check your chamber, practice safe range behavior and so on. You'll be surprised at how vastly different the various frame sizes and calibers are. You may also like shooting a .40, the recoil is different than a 9 or 45, generally speaking (I'd avoid a .45 "GAP" which is an oddball caliber proprietary to Glocks, you probably won't see many of these)
ALso you might want to consider the 357 - if you have a freiend that will let you shoot one you might be pleasantly surprised depending on your size/hand size.
As for good/not too expensive 380 depending on your hand size the LCP is a tiny little guy but very reliable.
Hope this helps a little. Oh and PS your grip is going to dictate your accuracy for starters, check out Jerry Miculek and Massad Ayoob, both are top-tier weapons experts and know how to hold a pistol right. There's drills you can do even with a pencil in your empty chamber taped to slide down your barrel straight, and "shoot" at a piece of paper on your wall. The firing pin shoves the erasered pencil down the barrel and pokes at the paper, and will help you determine if you are heeling, jerking, thumbing, pushing, anticipating, using too much or too little trigger finger, and so on, and it's free!