One moment in the future - people would read our FB posts, tweets, Instagram pictures as we now see the painting in caves. Our complete history, best moments, love, and hate would be part of this digital heritage. They would learn about us, how we did. They would watch our public communication, our private communication (there is no law to keep privacy after 300 years) and learn about us now. Complete our web sites would be probably at archive.org and similar sites. I guess the UN would be start a "digital initiative" to protect our digital heritage
It would be funny to see people like Data (Star Trek) processing 100TB of data and searching patterns and building a social network map (map that shows communication between people). Probably he would feel weird because he doesn't understand our funny posters and jokes.
In the 23 century, they would solve the economic issues - they would have no economy as we have now. The political system would be different and more efficient and with 0 corruption. Society would be developed. But still, they like to find traces about ancestors and how people live in 21 century. With the technology of that time, they would easily process yottabytes and filter what they need to know with AI. No regex at all. Probably there would be complete current internet on one small drive. Small like your pocket. And all data would be there. So one time in the future, all our data would be nonprivate and people would learn from them. It would be funny to see how they would get idea of how was in 21 century. So leave some message of love, peace, and hope.