The pre WW-2 versions as a rule are the most sought after. The rifles made after the war up until 1963 used to command a premium, and some still try to get it, but most should not be worth much more than any other 50-60 year old rifle in similar condition. Rare configurations and calibers are the exception, just as with any other gun. A common 30-06 made after the war just isn't that valuable anymore. Actually around $650 is about right for a post war common pre-64 in decent shape.
From 1964-1992 there were no CRF rifles made, and any pre 64 brought a premium just to get CRF during those years. After CRF was brought back with the "Classic" series made from 1992-2006 value gradually declined on common pre-64's. Winchester closed their New Haven factory in 2006. Guns made during the last 2-4 years can occasionally have QC issues, but are still a good gun. In fact in my opinion these are the best of the Winchesters.
The pushfeed rifles made 1964-2006 are generally good guns, but do not bring much money. $250-$350 depending on condition. Undervalued and a great buy for someone looking for a good hunting rifle for a good price. Especially those made after about 1980.
There is no good way to look up Winchester SN's.
An asking price of $650 is too much for any PF. If it is one of the Classics with CRF made in New Haven it would interest me a lot at that price. The early guns are generally better. If it has a 6 digit SN It is probably an early gun (1992-2000). A 7 digit SN means it was made in the last years. Most of those are fine too, but a few got out the door that should not have. I'd look real close at a Classic with 7 digit SN.