Learn English – “Will never write” vs “Would never write” vs “Never write”

Tom is the best expert ...

Assertion of a fact. Where there are agreed criteria then there's no need to hedge an statement.

Djokavic is the current number one male tennis player in the world

When criteria are less certain, or we ourselves are not sure of our facts, or we wish to be modest by appearing to be uncertain of our facts we may use I think

I think Djokavic is the best male tennis played of all time

I think that the population of the UK is 50 million (actually 65 million)

This formulation implies that we are open to correction and discussion

Adding would softens this further, emphasises that we are uncertain

I would think that the population of the UK is greater than 50 million

The I would have thought formulation is normally used in a context where some information has recently been given. Depending upon the context it may imply that we are actually contradicting the information, or that we are expressing surprised acceptance.

I think Tendulakar is the best batsman of all time

I would have thought Bradman had a better record

that was disagreeing, suggesting that by some criteria Bradman is better

The current UK population is 65 million

Oh, I would have thought it was only 50 million

but now I've changed my opinion (this implied but not said)

that was agreeing, I thought it was 50 million, but I accept your statement of 60 million is correct. We could just say

Oh, I thought it was only 50 million

With pretty much the same meaning, the slight difference being that the second case implies it was actively in my mind, whereas the would form could imply that I hadn't really formed a solid opinion until now, but I would probably have guessed 50 million.

As your comment indicates we are indeed into shades of meaning and idioms. In these cases the tone of voice will often differentiate the meaning.

I would have thought Bradman had a better record

Would probably said with a questioning or challenging tone and raised eyebrow.

I think you could simplify it down to this:

1. 'Want' is desire, and is used to express desire of some type. 'Will' has not lost its relationship to 'want,' as 'will' still has the context of "volition" or more simply, "will" (the two are synonyms). It however is not the same context as "do as what you are willing," in which 'willing' means something like "what you'd be comfortable doing, reasonably." It is not a want.
2. 'Shall' is closer to 'will.' It implies a lot of volition, more so than 'will,' which is conditional. It implies duty, just as 'must' does, but if taken in a modern context, 'must' is more informal and applies to a more flexible range of time.

If you need an example of 'will' in the more archaic context, here's one.