What should be the state site?

It so happened that our team has the opportunity to influence one large state website. Make a beautiful design, easy navigation, high-quality ideology. And it so happened that for us it is a free project. Money has long been drunk and not by us. Well, you know how it happens.

But we want to create a precedent in which real IT professionals will have the opportunity to do something decent for the state. Therefore, I appeal to you.
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Our task is to develop the design and overall concept of the site. Nothing more. This project is not funded in any way, but I am ready to allocate money from studio resources to pay for expert advice in the field of usability, design, building sites, etc.

I would like to hear the opinion of Habr on the following issues:
1. What are the current bad state sites? Where are their main shoals?
2. Do you know good government sites and how are they good?
3. What, in your opinion, should be the functionality of the state site?
4. What should be the design?

For convenience, you can imagine that we are talking about the website of the Ministry of Culture.

Please provide links and justify your arguments. Thank you very much.