"What should a city optimize for?"
I think a city needs to optimize for random interactions between diverse groups of people, which often is where that feeling of serendipity or je ne sais quoi feeling in a city comes from. There's no magic to it, you really just need to lay out your infrastructure to help allow for it.
In NYC we have it because of our public transit, mixed use/zoned buildings/neighborhoods, high density, small public parks spread out around the city, walkability, and a diversity of industries. We're losing some of that with the creation of bland spaces in the city [1], but I don't fear that NYC will lose itself anytime soon.
"How should we measure the effectiveness of a city"
It depends on the goal of the city. Are we attempting to make it a cultural capital of the world, like NYC and LA are, or a business capital like NYC and SF/SV are, or both? Or do we just care about providing a great place for people to live and work without much care for the city's perception in the world? Can it be just a nice second tier city like Boston or Seattle?
Personally, I'd aim for an NYC because there really is nothing like it in the states.
The effectiveness measures would also include some vague things, like influence of the exports of its cultural creations (art, music, fashion, tech). International desire to live or visit the city would be another metric. Then of course regular things like employment rates, educational standings, health of citizens, robustness of public transit, retention of citizens, racial/cultural/age diversity, surveyed happiness of citizens, etc.
Start with the art though. If your city doesn't produce a great diversity of culture it'll just stay a second or third tier city.
"How should citizens guide and participate in government?"
If you're building this city from the ground up you have an opportunity to immediately do away with the majority of the bureaucracy that holds most governments back. That'd encourage citizens to actually want to work with or for the government.
I'd avoid having armies of contractors and subcontractors. Create city organizations and workplaces that talented people want to work at, not stifling bureaucracies. Don't pay a consulting firm $600 million to build a payroll system that could be built by a small internal team of talented engineers, designers, and product managers. You probably will still need to pay an outside firm to, say, bore sewers and subway tunnels, but make sure the organization designing and overseeing it is staffed by talented people. That'd mean paying wages that match industry.
[1] https://aeon.co/essays/why-boring-streets-make-pedestrians-s...