I have built one OOB and some pics of it are here. Appears to be the first build on the net! 
http://www.modelshipgallery.com/gallery/bb/hms/hood-350-eb/eb-index.html  if I have done the link right
It appears that everyone else is gearing up with WEM or GMM etch sets and researching everthing before starting
Hmmmmm, I had a look on the Hood Assn website and the battlecruiser HMS Hood's paint colour was RN Medium grey in 1941.(AP507B)  
There are plenty of various images, paintings, graphics and a sample colour patch for an indication of the  correct shade, but then this also is affected by how accurately your computer monitor is colour managed as well as the Hood Assn's website. (It's a can of worms, my boy!)
I painted as much as I could on the sprues before beginning assembly. I used Humbrol Precision Poly to glue it all together. 
So, 50% Tamiya Dark Sea Grey enamel and 50% Tamiya Light Sea Grey mixed well and applied carefully by brush was my version of RN Medium Grey (AP507B).
Tamiya Buff for the the teak decks, then a touch over with a little smidgeon of red added to the buff to simulate weathering of the decks. Another my own brew for the corticene in the bridge,  superstructure (probably a little too red and new looking) and a little artistic licence with the rafts and boats to add a liitle contrast from the hull grey that they were actually painted and Bob's your uncle! Job done!
If one is aware of how light affects colours, the grey would be different shades at different times of the day and in varying weather conditions, include salt spray to lighten it up plus sun bleaching, and what is the correct shade of RN medium grey my son?
Nice kit to build, nearly everything fits well.  The deck at the tip of the stern needs a very fine trim to fit correctly ,as did the centre deck section on my kit at the starboard rear.
Take care to clean up the mould release marks on the back of parts to ensure a good fit without gaps
Not much trimming of flash was required and very little problem with the fine seams on some parts
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The turrents are not quite correct but look O.K. They can be filed to remove the sharp angles at the front  but not much can be done about the incorrect plating on the turrent tops. 
I used then as they came.
If you are a rivet counter, Foeth has made a 1/350 master of the correct style and these will soon be available as resin cast turrents from White Ensign Models
All in all It builds up into a very nice, highly detailed model straight from the box, that is of a higher standard than the twenty year old Tamiya 1/350 battleships, with quite a few fiddly little bit to keep you amused for a while.