Crusader Miniatures, Artizan Designs, Gripping Beast all make great 'levy' models with slings and bows. you can often mix and match between Norman, Viking and Saxon ranges (including kite shields IMHO) so I wouldn't feel too constrained about buying archetypal stereotyped nationalities. Gripping Beast to stirling work with their plastic 'generic' bow of Germanic warriors, alas without slings and bows as far as I know).
It's probably a common misconception that England "Knew not the bow" as the rest of Europe seemed to make good use of it around 1066. It's more likely that Harold had to leave his archers, who in general would probably not have owned horses behind in the race to get down to face William the Bastard threat.
My point is, all armies would have made use of the selfbow to some degree and it's really up to you as to what you think is historically correct based on the evidence out there.
I don't mean to sound like I'm on my high horse (I really don't want you to think I am being too haughty) but the information is out there if you look for it. The internet is actually your friend in this regard and there are plenty of books available on the various theaters of war that pertain to Saga. The Norman Conquest and other 'Periods' are well served, here's just a few samples:
Google books:
https://books.google.co.uk/books?id=5xnvEVqzUlMChttps://books.google.co.uk/books/about/The_English_and_the_Norman_Conquest.html?id=Su1IbQKzocsC&redir_esc=yhttps://books.google.co.uk/books/about/The_English_and_the_Norman_Conquest.html?id=Su1IbQKzocsC&redir_esc=y also, there is a great deal in print, for example, one of my favourite all time books is
The Byzantine Wars, John Haldon, which is a gem for the battles fought right up to and including Manzikert.
Darrell.