I read on reddit a few days ago that the 300 richest people in Athens would be the only people to pay taxes. Is this true, if so, were there any perks or social or otherwise? Was there a lot of turnover as to who belonged. It's a fascinating concept and I would like to learn more.

In general, Athens had other ways to gain taxes and revenue aside from the elite as the list of other answers below suggests, (ex. farms, slaves, mining, property ownership) but it seems like you want to focus on the way the elites were taxed.

Unfortunately, I don't have a source in front of me so I can't say if it was an exact 300 of the wealthiest Athenians who were taxed (My personal guess is that this was more dependent on weather an Athenian could pass a certain threshold of wealth along with the general demand for civic resources), however I can talk to the social aspects of these special taxes.

The rich Athenian elite that you're interested in were most typically subject to the liturgy. Rather than paying a specific sum the liturgy involved sponsoring some sort of public work, most often a trireme, a public building, or sponsoring the chorus at a festival. In theory, fulfilling one of these as a wealthy Athenian would be seen as a generous contribution to the state and would add one's public image and general prestige. Obviously though, the practice was not as simple.

Firstly, the levels of public fame from each liturgy varied. Sponsoring a gymnasium or a chorus generally gained you more recognition than sponsoring a trireme. The first two could be seen within Athens and contributed to life within the city while triremes often left the Athens for war and could easily be destroyed. As a result, the triearchy (τριηραρχία, the act of sponsoring a trireme) was the least desirable liturgy to receive.

On the other side, the choregia (χορηγία, sponsoring a chorus) was one of the more desirable duties. I haven't mentioned it yet, but the financial burden toward a wealthy Athenian was substantial at times. Tax dodgers certainly existed and people often tried to hide the extent of their wealth. However, many of the wealthy would often actively volunteer for the choregia. It was the cheapest type of liturgy, compared to a trireme or a gymnasium, gave public exposure, and the act of volunteering would only add to public image.

There's a lot more to be said on the topic, but this aspect of the liturgy shows a lot of the tensions between the Athenian elite and the state. My personal interest is how the citizenry actively tried to subvert the state and for that I'd recommend The Bad Citizen in Classical Athens by Matthew Christ. It deals a good amount in war and conscription but it contains a substantial chapter on the liturgy and taxation in general which I mostly pulled from for this post.