I would be onboard with reducing the pensions as well as the paychecks as a means to weed out those who are only looking to get rich but I don't know if public funding is the way to go. In essence you're talking about tax money...would that be an additional tax or would that be tax money taken away from another use?
We would ALL benefit so much if public policy were actually passed for the benefit of the country, the people, and even industry if we took out the professional lobbying groups. We lose so much money, productivity, and time by catering to special interests no matter who they represent. The amount of tax dollars spent financing these campaigns would be a drop in the bucket compared to what we lose through the current system. I also think that if you gave two presidential candidates 50 million dollars each and said run a campaign, we'd figure out relatively easily which one was better at managing public funds. Benefits such as pensions, health care, and any other perks should be the same as any government employee. That way they can't arbitrarily give themselves a benefit without giving it to everybody else in the system.
You would have to give all the Presidential Candidates the $50 million not just the Republicans and Democrats. Probably end up with 150 different political parties each with a candidate running for the office.