I shot the 14 in the service. A rifle with the finish worn completely off at any point you touch with your fingers. Bolts frequently fell out of the rifles during field training exercises and yet the guns shot extremely well. (So much time spent combing the grass for those bolts) I found no problem hitting the 400 meter targets from the sandbags. I thought I knew something about guns when I was drafted but the M14 excelled when it should not have. (We thought we needed bedded actions and free floated barrels of massive weight.)
It was a few years later before I could afford one, the
M1A that is, and then only on a stretch. I paid $526 for the SA M1A with new walnut stock. Still got it. And no, it is not for sale. Mostly GI parts on a new receiver and stock. One like that would go for $1500 (or more) in the box due to the large GI parts count. Later models with after market parts bring less. Chinese copies even less then that and I would not buy one at all.
The 14 is a very product improved M1, and really does not get the credit it deserves. The 16 was sold as lighter but after the military got through with it the weight is about the same as the 14 in the rifle version. The 16 will give you more ammo to miss with. I think we need more riflemen and fewer (P)hosers.
I do have an AR10 also and I think it better in many ways but the 14 is just so lovely. I would not like to have to choose.
Good luck on your hunt, and from my POV, buy the best you can possibly find.