camera buying advice

Hi guys, so let me state my background: I know nothing about cameras, I am just sick of having cell-phone quality pictures and want to have something with a lot more substance. Here's my deciding factors:

- size is a consideration but not absolute, I definitely do not want a bulky DSLR, but a pancake mirrorless would do fine. i,e it doesn't have to be pocketable.

- Image quality is the number one concern, I do not mind the camera is a bit expensive or a little large if the image quality can back it up.

- the main use of this (future) camera will be mainly snapshots, but it would also be an introduction/learning tool for more advanced photography.

- My max budget is about $700, but ideally I would like to spend around $300 to $400

I have been lurking the websites for a while and I still can't find answers for some of the following questions:

1. RX100 versus NEX series in pancakes lenses (in particular NEX-5/N/R), regardless of the size, which one has the better picture/higher IQ?

2. NEX-5N versus NEX-5R, a used NEX5N is significantly cheaper, is it worth it to get the NEX-5R if my only concern is image quality? (don't care about wifi crap)

3. Is there any compact point and shoots that rival RX100? I heard lumix LX7 is close.

Thanks in advance for whoever replies, also, I am open to any other camera suggestions.