It's easy to hand wave these things if you have read source material.
Players like myself are unaware of what books or authors to even search for.
Having even a vague idea of cost (rather than just "lots") is helpful.
Knowing that a Noble might have to get a loan
rather than just being able to pay out of general revenue
can generate more story hooks.
By the 13th century, royal power is becoming more concentrated making it harder and harder for nobles to just go to war off their own back. Also by this time, traditional feudal service of around 40 days for 'Knights Fee' (being considered to be the amount of land needed to support one knight - sadly not consistently defined!) was being undermined more and more by cash equivalents and the use of professional mercenaries.
These articles will be an initial help:
en.wikipedia.org/wiki/Knight-service
en.wikipedia.org/wiki/Knight%27s_fee
I really couldnt put a cost on this sort of activity, but I'm sure someone has. Sorry! Knights have a high start-up cost and expect to be fairly well kept while on campaign. Mercenaries would have had lower standards and were thus better bet in so many ways!