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
How I'd like to upgrade the system of Czechlands:
Bicameral parliament. The lower chamber is currently elected in a country-wide proportional ellections with electoral threshold of 5%, in name of easy established government. Let's get rid of the threshold.
But how would we get the government (currently must be approved by the lower chamber)? The lower chamber shall elect each member of government separately (and at will they shall elect a new one). This proces would allways result in an existing government. Some fancy condorcet voting method could be used, as I like fancy condorvet voting methods.
Upper chamber is currently elected in one-mandate districts by a two round system, I'd change it to approval system, as it has quite good qualities and is reasonably understandable (and trust is important in politics).