Disclaimer: Not for the weak of heart.
No, really, this thing contains ideas that are quite radical, and you're all likely to flame me to death for posting it, but what the hell.
Note: Obviously, everything would go down the drain very quickly with corrupt leaders, but i don't believe any system would work with corrupt leaders, so i don't see the point of mentioning corruption unless you have a way to end/reduce it.
Since we're all equals, we all have the same rights and deserve the same things. Thus, the best way to start off is to give everyone the same opportunities at birth. These opportunities should obviously be good enough to allow for any kind of life but moderate enough not to allow a person to have a good life without working. Everyone can choose what to do with the opportunities given to them, and thus a person who works hard will lead a great life and a person who chooses to be lazy will be poor and starve to death.
The obvious problem with such a system is what to do with the second generation. Eventually the people will grow up and have kids, and then a rich man's son will have better opportunities than a poor man's son, and it's not a kid's fault if his parents were lazy instead of productive. This problem is taken care of by eliminating inheritance. Thus, everyone has the same opportunities regardless of what their parents did in life (note: how to actually take this into effect (i.e. how to compensate from rich people's kids living in bigger houses than poor people's kids, for instance) is something i'm still working on, but the base idea is set). This solution also forces people into working for themselves and not for their kids, as their money goes into their own interests/needs instead of their children's. This has the side-effect of making people richer.
But knowledge is another kind of inheritance, some might say. So include an excellent educational system which teaches kids almost everything their parents could ever teach them, thus practically eliminating the advantage kids with intelligent parents would have over kids with not-so-intelligent parents.
Obviously, not everyone is a true equal. Some people are born with a genetic disease, some people are born smarter.... Well, some animals let their diseased/weak ones die and others even kill them, which ensures that the genetic "quality" of their population is kept at a high level. So why not us? With gene therapy we can already cure many genetic diseases, and i don't doubt that in the near future we'll be able to cure all or most of them (thanks to Zack for this idea). First of all, you improve the quality of life of these people
and the quality of life of their relatives and friends (as they don't have to waste resources on taking care of them). Second, some of these people are completely improductive and only drain the resources of a society, and their kids often have high chances of inheriting the condition, and all of this is eliminated/reduced by curing the diseases.
The government would provide quality services for free. These services would include health (hospitals, gene therapy, other advanced technology useful in medicine (such as embryo cloning for organ growing, stem cell research, etc)), education (schools and universities; they would all be public and have high standards for teachers, and private educational institutes would be forbidden), electricity+water+gas+whatever (with good resource management to prevent blackouts, water scarcity and so on), housing, and security (an efficient police force with instant and strict punishment for corrupt policemen and an equally strict punishment for criminals; for example, i don't think a death sentence is too much for a rapist or murderer, and i know i'm not alone in thinking that this is a sentence that should be used more; furthermore, the stricter punishments are the less likely you are to commit a crime). Education would include ethics and religion, but religion would be taught as knowledge, not as an attempt to convert kids to one religion or another (i.e. no religious schools would be allowed); in fact, although all religions would be tolerated (freedom of thought+speech), education would encourage (but not force) atheism. Religious institutes such as churches and temples would be strictly prohibited (the best temple is one's own house, or so a saying goes), and anyone caught trying to control a part of the population by preaching things or taking advantage of their beliefs would be arrested (after all, whoever wants to learn religion can purchase religious books; i've seen bibles for less than a dollar's worth).
Things like abortion, euthanasia and drugs would be legalized. Abortion and euthanasia are good healthy things; those in favor of abortion will do it even if it's illegal, and those against it won't start doing it just because it's legal, and if abortion is legalized then those who do it will at least have hygiene and controlled conditions and everything (which would greatly reduce the risk of infection and/or aftereffects). And if drugs were legalized then prices would drop and drug dealers would lose their jobs (after all,they're illegal: they don't pay taxes, they charge whatever they want, etc); and the same thing that applies to abortion applies to drug consumption: those in favor will still buy them, and those against won't, and drug consumption would be reduced because all those who only use them for the fun of doing something illegal would stop using them.
All kinds of science would be encouraged (with restrictions for scientists so that nobody makes and army of clones or builds nuclear weapons), and everything in the vein of astrology and scientology would be greatly discouraged. Patents are a great evil of society, i think, since 1) they let researchers sell their science/technology at ridiculously large prices and 2) they slow down research (the human genome project, for example, took longer than it should have taken because people would just patent gene after gene instead of working together and supporting each other), so they would be prohibited (but researchers/inventors would still get paid well for their work).
As all dictatorships are bad, there would not only be a leader (with limited power and no salary), but also a council (with no salary either). Thus, power wouldn't be divided into judicial, executive and legal (or whatever they're called) sectors, but into many sectors: science/technology, infrastructure, diplomatic relations, economy/ecology (see economy section below), education, national politics, public entertainment, etc. I'm still working on whether the leader should make decisions moderated by the council or the council should make the decisions and the leader should moderate. In either case, the council would consist of a representative for every major area (science, politics, education, infrastructure, economy, etc), and the representatives would be elected by a democratic voting system which would work as follows: People would only be able to vote for the representative(s) of the area(s) they are well-versed in (for example, an economist would be able to vote for the economy councilman but not for the education councilman, and so on). How the country's leader would be appointed i still don't know, but the idea of the previous leader appointing the next one (with the restriction that the previous one and the new one can't be friends) sounds attractive. All periods would last somewhere around 15-20 years, as i believe a 4-year (i.e. USA) or 6-year (i.e. Mexico) period is too short to actually accomplish anything. When decision-making time comes, all relevant people (scientists for science/technology decisions, etc) in the country (not only the councilmen) would be called to participate on a voting session, but not all votes would count the same; everyone would explain why they think a certain decision should be taken, and the councilman would act as a moderator and weigh the reasons given and make a decision based on that; thus, "i think cloning should be forbidden because it would just produce more mouths to feed" would have a greater weight than "cloning is bad because it goes against God". Finally, all kinds of political campaigns would be forbidden.
As for economics, i think
Judith's eco-economics system (with the added point that transgenics offer huge advantages) would work pretty well. I would also include a barter system rather than a currency system, but i'm no economist and any of you could easily prove the advantage(s) of currency over barter, if any, without leaving me much space to reply. But what's for sure is that economy wouldn't be anywhere close to where it is now in terms of importance, as 1) to make money your god is ridiculous, 2) i could debate extensively on the evils of capitalism, and 3) there are many things that are much more important in life than money.