Go full size
I guess I'm just old fashioned, but I like firepower if I'm having to jerk out my piece for self defense. I carry full size pistols concealed, and it only takes a little thought to be able to do that... inside the pants holsters, etc. to snug them up to your body.
I'm usually armed with a Ruger SR-9 (17+1) and two spare clips. Now, if we get into a "situation", I'm betting on my 9mm and 52 rounds, as opposed to your .380 and it's 7 or 8 rounds. I carry one of those "nearby" for backup.
If you're looking at .380's, I'd recommend a Walther PPK, PPKS or a Beretta. Their pistols are solid and easily concealable.
If you're new to concealed carry, you might want to invest some of that new cash in a few extra clips so you can carry enough ammo to finish a fight. As an ex-LEO, I firmly believe that extended shootouts go to the guy with the most ammo, and it's not uncommon for the first six or seven shots to go all over the place if you're not used to shooting under stress... like being shot at.
Depending on where I'm going and how I'm dressed, I often carry a Smith 4006 (11+1) and a couple of clips. That's a .40 caliber, and what I call a "big, ugly gun" for concealed carry. Looking down the barrel of that thing is like looking down a stovepipe... so it has a "fear factor" as well as firepower.
All of the weapons can be "helped" if you find ammo that's marked on the box either "Ultra shok", "for personal protection" or +P (just make sure your firearm will handle them).
If you're not a collector or have very many guns, your best bet would be to get both a concealed carry gun and a target pistol to help you practice shooting. There are a ton of .22 pistols out there that are also good back-up guns. I have a Walther P-22 and have run thousands of rounds through it, and if I'm just going out around the house, I'll stick that or my Beretta Bobcat in my pocket (another .22LR).
Concealed carry isn't just playing "hide a gun" with your clothes... it's a mindset you have to have. You need to practice, not only your shooting, but the different scenarios you might find yourself in where you need to use your hide-away. Shoot every week if you can.
What gun you carry will reflect your own experience in firearms and their use. Chasing fugitives and working undercover give you different ideas about how much you need to carry, and while I'm not a gun nut, I'm well armed and know how to use what I've got. You never want to come in 2nd in a gunfight... so make sure you've got enough gun to get the job done, and something light enough that you'll get off more than one shot.
Sorry to ramble, but I'm sleepy...
WT