"someone would put in complete charge of Nasa and give me a $25 billion/year budget. I'd do the following."

But NASA current budget is around 16 billion. Congress isn't giving current administrator that much, so why would they give you almost twice as much?

"Copy and improve upon the Energia/Vulkan launch system. Make it capable of putting 200 metric tons into Earth orbit in its maximum configuration."

That seems like a stupid idea. First you want to copy some Russian launch system that never existed? So, what do you do try to hire Russian engineers or are American engineers suppose to some how figure out it how they did it would have did it? Another point is America engineers actually built and launched the biggest launch vehicle with a 100% success, and you want to copy Russian? Third, you want the government to make and operate a ungodly huge rocket, for what reason? Isn't the shuttle program enough to show the folly of such idiocy?

"Build a second generation shuttle to launch on Energia"

I guess not.

"Build a manned capsule/unmanned supply craft to launch on the Energia."

Ok, whatever.

"Build a large orbiting space station (dual keel) for a 27 degree 600 kilometer orbit around Earth. It would be home port, shipyard, and testbed for new technologies. This station would serve as the gateway for the exploration and conquest of the solar system."

So having ISS is not enough, you want more of the same times 2 or more?

I'll skip the rest of it.

My solution, would be for the govt to try to open markets in Space.
My priorities would be to steer market forces so as to lower the cost of getting into space. I for example would design the manned Lunar program to encourage to production of private launch systems, such as what X-Space is planning on making and I would use Lockheed and Boeing's heavy EELV. This would cost less than NASA building heavy launch vehicles, so generally speaking I would be less than is future budgeted. I would save money, by not spending money- strange concept compared to idea that if you only spend enough billions you could somehow lower costs.

In addition and keeping with steering market forces, I would have a govt program that paid for water "test" payloads- I would as govt, offer to buy water payloads delivered to LEO or other orbits, at a low price, e.g. $500 per lbs to LEO. And buy at least 100 tons of these payload delivered. Cost? 200,000 lb times $500 equals 100 million. So that an idea of minimal spent over say a 5 year period, but instead let's allow about 1/2 billion over 5 years [average 100 million per year] and get over 100 tons, perhaps 200 tons or so and some or all could go to Non-LEO orbits.
I'm willing to discuss more details about this, but I have done so in the past so I won't do so at the moment.

Next, I would add to NASA's current budget IF by adding to current budget a lunar manned program could be completed in a shorter time frame. Add 1-2 billion per year to budget if the additional funds could speed up entire the process.

Second, I would make sure enough funds are going towards nuclear power use in Space.

Third, I would add funding that allow research and prototype work to be done regarding beaming power over large distance [though perhaps this should done in the Energy Dept or both NASA and Energy Dept could work together]