YA has limited the length of an answer, probably because of me ;-). Here are links to my answers that should satisfy your request:
For mostly 50s & 60s oldies, you may go a previous answer of mine that is about 4/5 down the page at:
https://answersrip.com/question/index?qid=20080313120342AAxhndD&show=7#profile-info-KLZECDIzaa
Also, check out the following link for oldies by year (and lyrics for many) from 1930 to 1999 and how they fared on the Billboard Charts. Any songs that peaked on the charts from #1 to #5 position (denoted to the right of the song) for any particular year may be worth listening to on YouTube and then downloading if you like it.
http://www.ntl.matrix.com.br/pfilho/html/top40/
For number ONE songs only, by year:
http://www.bobborst.com/popculture/number-one-songs-by-year/?y=1960&chart=us
Go to the link below to see the top songs for the decade you select.
http://www.acclaimedmusic.net/
You may also want to get a copy of Dave Marsh’s 1989 book, ‘The Heart of Rock and Soul, The 1001 Greatest Singles Ever Made’ from Abe books:
http://www.abebooks.com/servlet/SearchResults?an=dave+marsh&sts=t&tn=the+heart+of+rock+and+soul&x=0&y=0
If you scroll down at the link below, and look to the left hand side, there is a list of years you can browse through. It has a list of hit singles for the years to 2010 sorted into categories by the year.
http://www.popculturemadness.com/Music/