People are overlooking the "cheap" part...
Okay, so, people have already said, "don't skimp on something your life may depend on." I certainly second that. Moving on.
Based on nine years of selling firearms and talking to customers about what does and doesn't work, and seeing some of the ones that don't work come back to the shop, the issue you need to be concerned with, when buying the cheapest of guns, is whether or not the gun is going to blow up.
If you're going to go cheap, go Kel-Tec. Yes, they do feel like someone bought a toy gun and converted it into a real gun. They have a service life of ~6,000 rounds (which you're unlikely to ever reach, and, assuming a price of $15 for 50 rounds, 6,000 rounds of 9mm Luger is $1,800, just to keep things in proportion). Some may not feed properly right out of the box, but there are videos on how to do the very same refinement that Kel-Tec will do if the gun is still misfeeding after 200 rounds. You will also want to watch your mainspring (which runs down the back of the frame) for rust. I've heard of one Kel-tec that had a structural failing, and it was minor (the frame cracked apart).
SCCY, which is a copy of the same gun as the Kel-Tec P11, has had a bad habit of not properly headspacing their barrels, leading to some of them blowing up with standard factory ammunition. The last gun shop I worked for had a range, and one of their range guns was just such a SCCY. The headspacing was so bad that the nose of 115gr FMJ would engage the rifling, during chambering, so firmly that you would pull the bullet out of the case before you'd pull the whole round out of the chamber. It was a ticking time bomb. Blowing up was not an "if," but a "when."
That said, I do hear from plenty of people who haven't had a problem with their more recent guns.
Hi-Points are big and hefty, which is the only reason I recommend Kel-tec over them for the CCW purpose you stated. Most of them work, for a while, and Hi-Point will gladly make any of their non-working pistols work again. From some sources, it doesn't even matter if it's clearly your fault for abusing the gun.
Avoid Bryco, Davis, Jennings, Jimmenez, and Raven (this is not a comprehensive list, I just can't remember any of the other "ring of fire" companies, or their successors, off the top of my head) like the plague. Due to extremely poor manufacturing standards, they are all ticking time bombs. Even those that are .22 LR pistols have had structural failings whose catalyst was merely firing a cartridge.
Going up a bit in price will get you into the range of Taurus. Don't drop the semi-autos. Their drop safeties have been proven to be non-functional across several entire product lines, and they apparently don't care. In other words, make sure your holster's retention is good, and put it back in your pocket after using it on a BG so that you don't get ordered to drop it (cops get trigger happy when guns go off).
A used Ruger SR9c, SR40c, or LC9/LC9s shouldn't cost you more than $350, and that would be a good option. There are design flaws in these I don't like, but they're personal preferences, not things that can get you killed or maimed. The LC9s Pro lacks those design flaws, however, but they'll probably be difficult to find used.
On that topic, do not be afraid to buy used guns. Too many new shooters equate used guns with used cars, and they shouldn't. You're not going to get some half-functional piece of worn out junk because you bought a gun that's ten years old. With few exceptions, shooters take care of their firearms, and if they're taken care of, they can last centuries. Even if they're frequently shot, any gun of even intermediate quality can handle tens of thousands of rounds before anything needs replacing, and exceedingly few people will ever put enough rounds through a gun to ever need to replace something on it. Generally, when a used gun is in bad shape, it's still functionally perfect, but cosmetically degraded.
For about $400 to $450, you should start finding used or "low feature" new guns that are all excellent. Glock, Smith & Wesson M&P, Springfield XD, FN FNS/FNX/FNP, CZ, etc. Some may, as alluded to above, be in rough cosmetic shape, but will still operate flawlessly.
Also, while this won't reduce the price, many shops offer layaway, which allows you to spread the price out over multiple paychecks.