Various dictionaries have different things to say.
What price [fame/success/victory etc.]?
something that you say which means it is possible that the fame, success etc. that has been achieved was not worth all the suffering it has caused
What price victory when so many people have died to make it possible?
(Cambridge Idioms Dictionary, 2nd ed.)
price [...]
what price (something)? what are the chances of (something) happening now?
(Collins English Dictionary – Complete and Unabridged)
What price something?
What is the value of something?; What good is something? (Said when the value of the thing referred to is being diminished or ignored.)
Jane's best friend told us all about Jane's personal problems. What price friendship? Jack simply declared himself president of the political society. What price democracy?
(McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)
what price ——? used to ask what has become of something or to suggest that something has or would become worthless : what price justice if he were allowed to go free?
(New Oxford American Dictionary 2nd edition, from OS X)
Apart from Collins's strange definition, it seems that the general meaning of "what price X?" is "what's the value of X?" (not "what's the price of X", in the modern sense of price).
As for how it came to be, my wild speculation of the day is that it could have been used grammatically in an anaphoric expression, eg What price is freedom to us if we tolerate this tyranny? What price justice? etc.
Best Answer
To go to has a non-obvious secondary meaning of 'to perform', 'to undertake' or 'to try very hard' in a few common expressions that have a similar meaning to 'to go to great lengths', such as 'to go to a lot of effort' or 'to go to some trouble'.