I trust the people before I trust the government.
There is the problem. The people, in theory, ARE the government, but you don't see it that way and that is because the people are kept out of government as much as possible.
You can say that the government should be the sole supplier of campaign cash but you have the problem that you mentioned - that candidates can simply not be recognized and their funding would not happen.
Conversely is the problem that already exists, that the people who are in government happen to come from the same class as the people with all of the money and wealth. This means that if you could only approach friends and family and like minded corporations.
You couldn't run a people's campaign because the "people" don't have the money to run one.
The best you could do is outlaw all campaign finance and all campaigning outside of whistle stops and soap boxes. Further you would have to try to ensure that favours done in power couldn't be collected after the fact. It would be better to have a good permanent pension and outlaw any work for or money from companies permanently after serving in office than to dump pensions and therefore put it into politicians minds that they need to figure out what job they should get when done with office.
Certainly though, to make things more egalitarian, there should be no protection for politicians kids in times of war. Everyone goes to the front line - no deferments or favouritism just because your dad is rich or in Congress.
There should be no health benefit for politicians that isn't available to the general public.
But, mostly, instead of picking politicians brought to you by the slick campaigns paid for by Wall St and Texas Oil, the people need to pick their own representatives and stay off of those the media promotes. To have a people's government then people have to be actively involved in government every day. The people don't have the time and when they do have the time, mindless vapid and shallow entertainment is provided.
If the people turned off their television sets they would not be significantly less well informed, but they would be much less misinformed and they would have more time to work for real change. The amount of time spent watching the super bowl (and all the games that lead up to it) would be sufficient, if aggregated across the entire audience, to do significant damage to the ruling oligarchs.
The average American watches 28 hours a week of TV. That's a part time job. Working 4 hours a day on almost any political agenda would, over a year, either get results or get you on the no-fly list. Either way a better use of time than watching millionaires chuck a ball around.