If your going to get a CC , your probably going to need the background check. Although a call to your county clerks office could probably point you in a better direction pertaining to your local laws. Here in NY thats pretty much where you start the process.
Now on to the gun. I've been collecting for about 25 years and own a lot of guns , so what follows is just my experiences and hopefully may be able to help some. Bear in mind that some modifications are simple "drop in" stuff that will help, and some require machining. We've owned a machine shop for a number of years and were able to do the work ourselves , but I also had the advantage of having my dad who was an accomplished toolmaker and gunsmith to learn from , so dont go breaking out the Makita grinder and a set of files and think some things will work. Theres my disclaimer, hehe.
First off , join a gun club . It does two things. 1- gives you a place to safely shoot in a controlled atmosphere. 2- most good ones will have an instructor which will not only help you in the safe handling ,clearing and carrying of the gun,but will also kinda help you decide on the model
which best suits you (size , concealment, ect). As for the caliber , it all depends what your looking for. If its for home defense , and you live in a small house, you'll want stopping power over accuracy. 40 cal or 45 cal are unrivaled in this department imho. The XD Wolf suggested is a fine handgun. I own one as well. I swapped out the trigger , guide rod , barrel, and locking ring , and replaced the barrel bushing with a suppressor and can unload 5 shots into a 5" pie plate standing at 35-40 yards no problems. but the gun is heavier and longer, so there goes concealment. I think the 40's a bit more accurate for longer ranges/ larger house.(read below)
My other standard Colt 1911's (or any good brand of the same gun, there are a ton of them) are a better concealed weapon and can easily be modified in many configurations to fit the owner. Things like left/right safety tang , grips, sights , ect all play a part in how it
works for you I also own a Taurus 40 cal..and its quickly growing on me. Its more accurate (imo), and has just as much stopping power with the right ammo. But is a little harder to control being on a smaller frame but conceals better. In my experiences I've tried a few different 9MM's , and just say they are nothing like the ones ingame. They all seem to lack the range and accuracy of just about anything else. the Glock 17 I had was traded for the XD I mentioned even after reworking the gun ($$) to be marginally as accurate and comfortable as the stock XD. But in your situation it may be acceptable. There are a ton of cheap ones out there , and if price is an issue, you may want to look at those.
So you see there are many variables. Get with a good reputable gun dealer and explain exactly what your looking for , what you want to use it for , and what you expect out of it. A good dealer will take the time and make sure your comfortable with your purchase , he wants you to come back. I usually avoid buying guns at Gander Mountain type places because they usually lack the experience and knowledge a good dealer will have.