I'm a fan of MMP voting (used in Germany, New Zealand, and the Scottish/Welsh parliaments in the UK), where you vote for a district representative and a party and the parties get extra seats to ensure that the proportions balance out. It's easy for voters to understand - no ranking or rating or whatever - and it simultaneously lets you support third parties (because they'll get some seats even if they don't have a majority in any district), lets you vote for the best candidate in your particular district without regard to their party (if you like your local Republican but you hate national Republicans you can simultaneously vote for your guy + for him to be in the minority), eliminates gerrymandering (since party representation comes from a percentage of the overall vote), and makes every vote count (since even in a deep red district your blue vote still contributes to the national total for your party and therefore its share of legislative seats).
If that proves successful then we can explore other systems for national/presidential votes, but you're never going to get a serious third-party movement in the US if you insist on starting with the White House - reforms to support third-party presidential candidates are the sort of thing you do after you've got 40 or 50 minor party representatives in Congress.