All money raised by all candidates goes into a pot and is then distributed equally to all candidates, or the top 5 at least. In this way, money cannot unduly influence the results by having someone with a multiple million dollar war chest simply swamping someone with a much smaller war chest.
I also think that war chests should be limited, to limit the influence of money on politics. Not sure how to do that, though, except by above.
First, pick a system and stick with it. Since there are laws against making a person show or tell their vote, this means that caucuses should be done away with (as they are a very public way of voting, where everyone in the room can see for which candidate you are choosing to vote). Secondly, all primaries should happen at the same time, across the nation, rather than over months. This gives no undo sway to any particular state and means the candidates have to travel to most states and get their message across equally.
Registered independent voters should get special ballots that show all candidates on it for a primary.
No results from any primary or election may be reported on or disclosed in any way prior to the last polling place closing. In this way, the east polls cannot influence the west's voting. Everyone can simply wait until the next day to see who won/lost.
The election is held on the first Tuesday after the first Monday in November (note: the wording is complicated because the month can start on a Tuesday or later day). This means the election is held November 2 through 8th, depending on when that Tuesday falls. I don't see any reason, whatsoever, that an election cycle, from declaring, to primaries, to DNCC/RNCC, to election, needs to last longer than six months. So, candidates must declare no later than May 1st. The primaries should be held two months later, in July, and the winning candidates would have four months to debate, set their agendas and platforms, and campaign.
The act of voting needs to be made more simple, but also as error-, fraud-, and influence-free as possible. Voting via the internet is an absolute requirement. I mean, if you can do your taxes online, you should be able to vote online. No matter how they vote, all votes should get a physical copy of their results in case of suspected fraud, by which they can verify who they voted for. For example, if you vote online, you should receive an automated email response that shows "These are the candidates and ballot measures you voted FOR:" and a list. If fraud is suspected, the voting commission can ask the voters in that area for their confirmations, make a copy, and recount the votes or check the results. This should happen with electronic devices at polling stations, or manual processes, as well.
We need to change the laws to do away with gerrymandering. By changing the district shapes and locations, parties have made it almost impossible for an incumbent to not get re-elected. We need politicians to have to sway voters of all stripes, so their districts should have a good mix of all parties in it. This moves everyone back toward the middle, rather than polarizing, and means we have a Congress and other offices that can work together, rather than a divisive group of far right or far left people who refuse to work together. Compromise is possible. It also means you may have a Democrat win a district that is predominantly conservative, and his/her message and voting record will have to reflect the population and the will of the people he/she is representing, rather than her own politics.
I think these are a good first step toward making the election cycle shorter and more fair. It makes people running for office have to actually campaign and it levels the playing field between all the candidates. I think you would also see the general public invest more of their time, effort, and interest in the election process, and would see a commensurate gain in voters each cycle. There may be more ideas that can be added that would further tighten up the election process. I'll add more as I hear, or think of them.