"But there's one thing that's impossible to fathom: what will astronauts feel when they won't be able to see our planet (blinded by the sun glare)? Maybe a moonbase on farside will be an interesting way to test this! "

Well I rather build a base in the shade- it's easier to make heat than shed it. And if you are standing at the lunar poles, you can have a situation where the sun is behind you and Earth is in front of you.
I disagree with Tom's statement about a lunar base being built first. NASA should explore the Moon for minable water, this doesn't require "a base" to be built. Focusing on building a lunar base, will probably be a distraction from NASA exploring space. It *might* make sense to build a space station in high orbit/L1, this could be more for Mars Manned than exploring the Moon for minable water.
In summary Lunar exploration should be a big ticket item, it should be less than 5 billion. A station at L1 would be different budget and could be in the range of +2 billion (depending on what is exactly was and how much time was spend running it- it could be easily be around 10 billion or more).
If it was up to me, I would buy water test payloads. Start doing it yesterday. This is super cheap & could be very useful as far as opening up space frontier.
Next, I would have NASA explore the Moon for minable water deposits. This would use the private sector. It would involve the private sector. It would involve companies who are currently not even considering space as something they have an interest in- these would be mining and oil companies and others. NASA should get a program for exploring the Moon. It would, of course, start with using non-crewed exploration and would most likely finish with Manned exploration. With a framework of how to do this for less than 5 billion, NASA would then show this, to public and ask if private sector wanted to do some of the functions of this program- on mostly their nickel, but could be subsidied by govt in some manner. In other words the private sector could be offered to be part of the program, and NASA would "help" to the extent that what they wanted to do, aligned the the purpose of finding minable water.
In other words, this NASA program is NOT about providing something for NASA empoyees to work on [a job's program] it's about determining if there is minable deposits of water on the Moon and "trying" to involve the private sector with the program [so there is also a greater chance that they will latter "independently" set up operation which are in involved with mining water or other commerical interests].
A considered prerequisite for a Manned Mars should be that there is some commerical development in space. The miminal could be simply be a gas station in LEO or L1. Or even some tug service for GEO satellites. What would be really good would be some company starting mining on the Moon- we need markets in space, once we have one market in space, other will probably develop and the cost of getting into space will be lowered.