You have to decide that you are going to make a commitment to a lifestyle in which you do EVERYTHING you can to keep yourself safe. Not just carry a gun. Ditch your dangerous friends. Don't go to bars where there are a lot of fights. Don't enable and indulge friends and family members who are addicts. Check the batteries in your smoke detectors. Get some umbrella coverage liability and life insurance. You must become a person who is always aware of your surroundings and options. If you aren't willing to do these things as well, it doesn't make much sense to carry a gun.
You must commit to carrying everywhere you legally can. If you don't, you open yourself to liability in a situation where maybe you shouldn't have gone there, but instead you put on your gun and went anyway.
And you are right to assume that if you use your gun and the police are involved, it is a very real possibility that you will never see it again.
Don't put a dollar value on this. Certainly not one that low. Yes, you can find a good used revolver or Glock in that price range, but you are talking about your life. You need to find the gun that works best for you, REGARDLESS OF PRICE, and stick with it. If you don't it sounds just like buying used discount fire extinguishers and hoping for the best. When you REALLY need to use it, the last thing that will go through your head before you pull the lever is; "I feel really, REALLY stupid right now for not buying the better one." It's the exact same thing you will think if you buy a cheap gun and have to use it.
You need to go to a rental range and shoot a LARGE variety of guns to see what one works best for you. This will cost you some money for range fees and ammo. Spend it anyway.
Here's the bottom line for why we carry. (I think I can speak for most of us.) YOU are responsible for your safety. Legally, ethically, and according to common sense. If someone is trying to harm you, the police can't get there fast enough to help you, and if they just don't come, THEY ARE NOT LIABLE. They will take some pictures and write a report. Whether or not they catch the bad guy doesn't do you OR YOUR FAMILY any good at all if you're dead. Self-defense is a fundamental human right. You must embrace it and exercise it as you should ALL rights.
And since you mention it, I have been in a situation where I saw a deer get hit, it was suffering, and I put it down. But it wasn't near an incorporated city. Just because it's the humane thing to do doesn't mean you won't get prosecuted for unlawfully discharging a weapon in city limits.