Personally, I'd like to see an expansion of literal democracy. I'd like to see more issues open to public, national vote.
We have the technology to make this happen. An increase in access/influence in regards to legislative issues would probably create an accompanying increase in civic investment, literally, emotionally, and practically.
I agree with much of what has been stated above. I would keep a democracy much like the United States currently utilizes. I would institute the following changes:
1. Extreme campaign finance reform to eliminate corporate influence in politics.
2. End of the electoral college system.
3. Term limits in the Senate, unless elected with 80% of the vote in that person's last term.
4. Extension of the term limits for President if elected with 80% of the vote in their second term for an additional term.
5. Six month campaign MAXIMUM for all offices.
I do not feel at all qualified to determine this. However, what I do not like about the current system is that it is too bipartisan. Everyone is only interested in elections. Politicians always are either worried about not getting re-elected or are campaigning for re-election. Either way they are not focused. Those ineligible for another term because lame ducks. Either way it’s ineffective!
I would love to see democracy with a capitalistic economic system, but some kind of required national service (not necessarily just a a military draft) that could be geared toward helping underpriveleged or underdeveloped areas. One of the weaknesses of our system is that a group of people is always left behind economically and politically.
The best political system possible would be one in which there was a philosopher king. Democracy does not work well enough to be called ideal. I would set up a system in which the wisest person (don't ask me how we'll find that person) would be appointed ruler. That way we could actually get things done even when the people did not want those things done (like how we need Social Security and Medicare reform but won't vote for people who would do that).
Aside from the great points made in the first response, I will just add that I would include some sort of structural features designed to limit corporate influence on policy. I would also be careful to actually lay out procedure for legislative procedure, so as to avoid filibustering and other parliamentary tricks.
Your question asks about the "best political system" I could create. In my ideal world, there would be a difference between the political structure and the economic world, so I won't be addressing your economic equality tag in my suggested system.
My political organization would be based upon a one-person-one-vote representative democracy; voters would elect representatives to do the work of governing on their behalf, but I would find a system of educating voters about issues and insuring that all potential voters did participate in the process of electing those representatives.
There would probably be term limits in my political system so that representatives remained closely responsible to the electorate. Seating, assignments, and other delegations of authority would be arranged to insure that representatives were not able to isolate themselves from other representatives, but would be highly encouraged to talk and negotiate and cooperatively focus on governing for the benefit of the nation as a whole, not for small or narrowly influential interest groups.
Individual rights would be broadly defined and protected by the legal framework of the government. Freedoms of politics and religion would be included; prohibitions would be in place against discrimination based on race, creed, sexual orientation, educational level, physical or mental handicap, age, or other such criteria.
Of course, all of this is easy to say in theory; it's much more difficult to make it actually happen in the real world!