i started out doing asm on my ti-83 plus, no emulator which sucked a lot because I had to upload everytime to test my code. In college i learned i386 assembly which was cool, but icky. It's not something i would program in, but knowing assembly a useful skill for debugging and the like.
I'm not sure what stuff there is for c64 in particular, but something with an emulator and fairly popular (i.e. a processor/computer that is still made and used) is a good place to start learning assembly. Hobby robotics is also a fun place to look into, though some of them may not have emulators. Although some things in robotics are done in basic or c, there are still a bunch that use pure assembly. Popular cpus include z80, 68k, 8080, i386, and vairous pics. The simpler the cpu, the easier it is to learn. i386 is very complex compared to some of the others so i would stick away from that for now unless you are very determined.
Early consoles can be a good place to start, esp nes/snes where people have made many home brew games for them.
http://www.grandtheftendo.com/ is an example of something crazy someone has done for the nes. I'd kinda be tempted to do nes first becuse the guy at the link wrote a ide for nes assembly. If you do choose the console route,
www.zsnes.com has links to emulators as well as documentation on the system. If you choose to program calculators,
www.ticalc.org has lots of information. Any other route, google should be able to find info for you.
Good luck!