The first thing I suggest is getting your CPL before you buy your gun. Chances are you'll eliminate any waiting period, and they usually have a unique identifier to help you pass your checks. I always prefer walking out with my purchase to walking out with a promise to come back in a few days while they keep my money.
The second thing I'll suggest is you reconsider a 22LR pistol for target shooting- a 1911-22 target pistol is wonderfully fun to shoot, and the little bitty round in a frame that substantial won't feel like much at all when it goes off. Additionally a box of ammo (say .45ACP since that's what I hunt Walmart for) will run $30-33ish for a 100 round Federal value pack... IF you can find them. Basically every time you pull the trigger take a dime and quarter out of your pocket and tdrop them in a wishing well. I think a 550 pack of 22LR is about 6 bucks and change... Fire twice and drop three pennies on the ground. Use the money you save to buy a SD pistol when you're ready to carry. After you use the first couple 20's you save to buy a boresnake type cleaning device, and combination cleaner/lubricant/preservative type cleaner generically called CLP, not necessarily the brand name CLP- and whatnot...The gun isn't expensive, it's maintaining the gun and your range time that gets you.
Since your right hand is less than 100% keep that in mind as you buy your first gun... safety? No safety? (I wouldn't recomend it, but it's your choice) Ambidexterous safety? If 350 is a hard limit, you don't have the money to pay for an aftermarket gunsmith-installed modification so it should come with the safety style you want/need.
Additional costs: A holster for concealed carry when you're ready. Expect to drop at least 100 on a conealable holster. For maximum concealability, you want an Inside-The-Waistband or IWB holster, or a pocket holster if you get a snubby little thing. Do not get a wallet holster with an opening for the trigger if you get a baby pistol, that becomes an "Any Other Weapon" and you have to pay extra to the ATF for that, or pay a LOT extra when someone finds it on you...
If you get something big enough to wear on a belt, get a gun belt, whether you use IWB, or Pancake, or Paddle. You can get a Gould and Goodrich fairly cheap on Amazon. Yeah, finally we luck out somewhere. Though it doesn't look great, it doesn't look bad, and great costs a hundred or better. Shoot an C pasters from Amazon for the easy to discern target shooting results are also cheaper on Amazon.