Leading questions:
Representative vs Direct Democracy?
Unitary or Federal?
Presidential or Parliamentary?
How much separations of powers should there be? In presidential systems, such as the United States of America, there is often deadlock between the executive and legislature. In parliamentary systems, the head of government is elected by legislature, therefore, there is practically no deadlock as long as theres is majority support of the executive in the legislature (although, there can still be courts to determine constitutionality of policiss). Would you prefer more checks and balances, but can also result in more deadlock, or a government more easily able to enact policies, for better or for worse?
Electoral method? FPTP? Two-Round? Ranked-Choice/Single-Transferable Vote? What about legislature? Should there be local districts? Single or Multi member districts? Proportional-representation based on votes for a party? If so, how should the party-lists be determined?
Should anti-democratic parties be banned? Or should all parties be allowed to compete in elections, regardless of ideology? In Germany, they practice what's called "Defensive Democracy" which bans any political parties (and their successors) that are anti-democratic. Some of banned political parties include the nazi party.
How easy or difficult should the constitution br allowed to be changed? Majority support or some type of supermajority support?
Should we really elect officials, or randomly select them via sortition?
These are just some topics to think about, you don't have to answer all of them.
Edit: Clarified some things
My one: a bicameral parliament, with a lower house (like the US/Australian Representatives or UK Commons) doing most of the legislating, and an upper house of review (like the Senate or Lords). The lower house would be elected by a system of proportional representation, resulting in predominantly negotiated coalition governments as in continental Europe. (The layout would be hemicircular to facilitate this, as opposed to the Westminster layout of two benches facing off.) The government would be parliamentary, led by a prime minister who would appoint ministers (which would often be as per coalition negotiations).
The lower house’s electorates would be geographical, with each citizen living in an electorate with one or more MPs (having two, typically from different parties, could mitigate political minorities being unrepresented in their electorate). The upper house would break with this, but, unlike the Lords, would probably be elected. It could be geographical (as the US/AU Senate, with a number of Senators per larger region), or by some other division (perhaps different groups with specific interests and perspectives: industries, unions, young/elderly people, people with disabilities, remote regions, &c.). Alternatively, part or all of the elected upper house could be replaced with a system not unlike jury duty, where a number of randomly chosen citizens are drafted in to oversee the process for a period; hopefully in sufficient numbers, individual flaws would balance out, leaving a broader scrutiny of and input into the legislative programme.
There would be a head of state, who would be a ceremonial figurehead and largely apolitical, with no executive power per se. They may be popularly elected or appointed, and their terms would be longer than a parliament, providing a sense of continuity. Ideal candidates would be figures held in high esteem by broad cross sections of society; celebrated writers/commentators or other public figures, for example. Perhaps the role would absorb some of the duties of the poet laureate as well.