If this is your first radio project, I'd recommend something like a 1950s Zenith AM/FM to get your feet wet. If you can successfully recap that and get it working, you can move up to a Grundig. European radios are often very good performers, but I wouldn't call them easy to work on. The construction is often cramped, with smaller components than American radios.
In many cases, all an old radio needs is recapping and cleaning of the controls with DeOxit. This article gives basic advice about recapping:
http://antiqueradio.org/recap.htm
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html