Man, I just love those old 301s! I recommend them to everyone who wants a reliable portable machine. So cute ... and a much better value than a FW. As I recall, the serial number is stamped onto the bottom of the machine, over by the turn wheel. Then again, it could be over by the needle. Wherever it is, it's not hard to find.
Sounds like it came from a flea market or somesuch, but does it have any attachments? One of the first things I bought for mine was a 1/4" Bigfoot.
Congratulations on your Big Find!