I'm looking to buy a camera

Perhaps this belongs in a different board, I don't know. Nevertheless. I'm looking for a camera. I enjoy taking pictures of people and things, but for a while have been stuck with my (terrible) cell phone camera. The contrast, brightness, and resolution is poor. There is one thing I like about it: it is small and actually somewhat concealable. If I want to take a picture of someone that I don't know (don't get the wrong idea about me doing that), a phone is very inconspicuous. I can just hold it up and pretend like I'm checking a text message or something, and take a picture. Despite that, I'm not sure I want to buy a new phone for the purpose of taking pictures, so anyway...

Ideally, my camera will be small and could fit in my pocket comfortably. Secondly, it will take good pics. I have 0 experience with digital cameras, so I have no idea what type of features I should be looking for regarding quality in a camera, so maybe you can help me out. Thirdly, it will be not incredibly expensive. Hopefully less than $300. Since the first two requirements conflict with the last one, I'll have to make some compromises with the price, size, or features. I just want to get a rough idea of what I should be looking at.

Jam it back in, in the dark.

Oh, apparently cameras are computers and/or computer hardware.

There's nowhere I can't reach.