Keith,
Real Band, Audacity, Goldwave all will do the trick.
I would, however, recommend the purchase of a better tape deck, though. Remember that these are priceless memories, and they are only going to be as good as the player that you use to record them from. An old Cassette player that has only speakers or a headphone out is not going to be the best to play back your old recordings.
I would look around in your local stores and such for used decks. Also, you want to make sure the tape head is cleaned, aligned, and that the tape transport is also clean and free of debris.
I would look at some higher end units on ebay, such as this one:
http://cgi.ebay.com.au/Harman-Kardon-TD4...=item2a055480a9or, this one:
http://cgi.ebay.com.au/YAMAHA-SINGLE-CAS...=item3caae38950or:
http://cgi.ebay.com.au/Denon-DRM-510-Cas...=item439dc33f20Anyway, you get the picture. To assure the best playback, on units this old you probably should consider investing in new belts for the drive assemblies, which shouldn't be that hard to replace.
I think with that, you'll be very pleased with the results you get from transferring your tapes to digital.
Gary