My preferred method: Get rid of districts, and give the power to the voters. Set a window for 6-3 months before the election, and everybody registers their party preference. So, for a Federal election May to July, voters select the party they want to represent them. Maybe you end up with half Republicans and Democrats, and other parties finally get some real representation, collecting the other half. You use the registrations to determine which parties will get how many candidates. (Say 120 for Republicans & 120 for Democrats, 50 Libertarians, 45 Greens, 5 Communists, 3 Anarchists, 25 NAACP, 25 Latino Party, 1 KKK, 25 Christian Conservatives, 10 AARP, 15 Peace Party, etc.) Then once each party knows how many spots, they have their own party elections to determine which candidates they want to represent their constituents.
You have added benefits where everybody has a better selection than current. If you decide you don't like your current party (corruption, anti-science or education or other divergences) try to build a following to pull the party in a new direction, start a new party, select from dozens of other options.
You get rid of having half of a district feeling like their representative works for somebody else.
You get rid of the alignment between the Senate and the House, where they are chosen by the same electorate, just with fewer seats. Actually, we should throw out the Senate and have the State Houses approve the bills passed by the Federal House, before sending it to the President. Given today's technology level at the time of the negotiation of the House of Representatives, we probably would have had this instead of Senators, who were supposed to represent a break on the Federal government over running the powers of the states. All responsibilities of the Senate to approve Treaties, Presidential appointments, and impeachment duties are turned over to the House.
Then, since the electoral college is supposed to be somewhat representative of the House and Senate, replace it with the newly elected House plus the governor and his lieutenant governor, and throw out the presidential election altogether. This will reduce the cult of personality that gave us both Bush and Obama. Since the parties will be more fractured, the elected representatives will hopefully compromise on a competent candidate that doesn't upset anybody too much.