The only system I know of that avoids these problems is to hold randomized lotteries for government positions and skip the election process entirely.
Simples steps, clearly communicable steps, and one step at a time.
Start by Reducing the impact of money on elections. Politicians themselves will thank you.
The ability to flog oneself on the airwaves, to call and reach out to people and keep targeting newer and newer potential voters. These abilities force politicians into a monetary arms race.
The easiest thing here is funding, and curtailing it.
The issues are creative ways to get on the air without resorting to using money.
But one step at a time.
The changes are not mutually exclusive, either. Let's reform voting and reduce influence by money in elections.
https://www.youtube.com/watch?v=s7tWHJfhiyo
https://www.youtube.com/watch?v=e3GFG0sXIig
https://www.youtube.com/watch?v=Erph1L_XwVQ