David Nicolles 2 Volume work "Medieval Warfare Source Book" is probably my favourite in terms of military. It covers virtually everything between the 4th and 14th centuries.
Check out both volumes here -
http://www.amazon.co.uk/exec....9761248
Can't help you too much on the culture stuff - not really my area (do a search on Amazon and have a read of some of the readers reviews - I'm sure you'll find a lot).
However, two books I especially like are Michael Woods "In Search of The Dark Ages" and "In Search of The Doomsday Book" (published by the BBC). I bit specialised but very readable and covers all aspects of "culture" in this periods.
In fact all of his "In Search of ..." series are outstanding. Not to be missed
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