The absolute best action you can take right now is to attend a two day defensive handgun class. You do not need to own a gun; gun schools have them available for rent. The reason is if you are not a dedicated handgunner, you
likely do not know what you need in a defensive gun. A defensive course will show you what is necessary and what is not.
I do not know your skill level with handguns. It sounds like you are rather new (meaning you haven't fired 10,000 rounds in the past year or two). On demand, can you quickly shoot two ten round groups at two different targets 15 yards away and and keep all shots within three to four inches? Can you hit a 3x5 note card, slow fire, at 25 yards on demand? If you do a double tap, do both rounds consistently hit within one and a half inches of each other at seven yards? If not, then a small handgun is not what you need because they're not good learning guns. Purchase a mid to full sized gun. You can buy a small gun later.
That said, if you have to have a gun NOW, then the default choice is a Glock 19 with night sights. The gun is a great balance between sight radius, weight, capacity, size and so forth. It is easy on the hands and the magazines are durable. The guns are reliable and shoot well. They need not be modified other than to change the sights.
Do not fool around with 1911's or revolvers. Do not purchase a snubby revolver under any circumstances. Revolvers require quite a bit of dedication to master shooting and reloading.
Revolver instructors are difficult to find and do not attend a class with an instructor who doesn't know them. If you must have a revolver, buy one with a four inch barrel (I like the Ruger GP100 over the S&W revolvers for a variety of reasons). 1911's are another level dedication that requires you know what you are doing (google 10-8 Performance and read the duty 1911 articles for a glimpse of the "fun" 1911 guys have). Stick with service guns from Beretta, SIG Classic P-Series (P220, P225, P226, P228, P229, P239, P2022. Avoid P250, P224, P290, P227 (too new)), HK, Glock, Springfield, S&W and Kahr. There are other brands that are good, but these stick out as the top brands.
You should have no trouble concealing a Glock 19. Get a holster with good forward cant to mitigate printing out back. Buy a gun belt and two single magazine belt holders (DeSantis FTU holders work well). If you insist upon a small gun, then the Glock 26 is an excellent choice. I find mine to be very accurate and you can use Glock 19 mags with them.
Glock 26 with Glock 19 magazine and A&G Grip Adaptor
RE: Remington R-51
It is a new gun and there are bound to be bugs. Do not be a beta tester. Wait two years before purchasing one. For defense, buy something with an established track record. I have jumped on the bandwagon too many times only to wish I had that $500-600 back.