I am being out of place posting of my Aunt's obituary in the newspaper entirely paid for me?

No, its thoughtful and respectful.

Don't even worry about it. Nobody reads the newspaper anymore. There are plenty of obituary internet sites which are seen by more people than the daily newspaper. And I would not pay $500 to have a mention in the newspaper that nobody is ever going to freaking read

It depends. Usually it is the immediately family who does it (husband, or children). My Step Fathers Niece put an obit in several newspapers, they were not correct AND he had not wanted one. Since he was my father for 33 years, and I lived with or very near him, I was more than miffed. If you do, you might want to ask if your Aunt specifically didn't want one.