You realize that the 201 is one of Singer's most coveted machines. All vintage lovers are looking for one. It may be Singer's finest machine. Congratulations.
The Singer company kept good records and the serial number will date it - except for a few lost records. Here is the site. After you look it up on the left column, use the right column to go to the next page and get more info.
http://www.singerco.com/support/machine-serial-numbers She was born in Nov 1956 in Elizabethport, NJ, so it's not a very old machine. Happy sewing.