Want money out of presidential politics? Make everybody run using only the presidential-campaign fund. You know, that one that you check the box on your tax return to give a couple bucks to?
As for Congress, we also already have a good fix, we just never got around to passing it. Congressional politics are full of money because the districts are too large, on average. The districts are too large because in the 50 states, with 320 million people, we have only 435 voting members in the House of Representatives.
The solution is more Representatives and smaller districts; when you don't have to run a campaign in multiple expensive markets across a broad area, you don't need as much money (and can get to know your constituents better).
And it turns out... there's a constitutional amendment for that.
Way back in 1789 when Congress met for the first time after the Constitution went into effect, they submitted twelve amendments to the states. Ten of them were ratified quickly and became what we know as the Bill of Rights. The other two were not ratified by enough states, and were mostly forgotten.
Today, it's common for Congress to put a time limit on an amendment, saying it has to be ratified within X years or it's dead. But back then they didn't do that. So in 1992 a random university student discovered one of the two "forgotten" amendments and that it was still legislatively "live" -- it would take effect if enough states ratified them. He campaigned hard and got the amendment (which says any increase in salary for members of Congress doesn't take effect until after the next House election) ratified, as the 27th amendment.
The other one is still sitting out there, and would become part of the Constitution if enough states (currently, 27) would ratify it. And it changes the formula for how many Representatives there are, and how they're apportioned. The original text of the Constitution set a cap on the size of the House of Representatives, at one Representative per 30,000 people. The apportionment amendment would raise that to 1 per 50,000, and the version passed by the Senate would require increasing the number of Representatives as the population of the US grows.
So if you want real change in Congress, campaign to get the House of Representatives enlarged. There's even already an amendment available to help you, if you can get it ratified.