Well, thinking back a bit..
defintiely Wildwood Flower, in G, with the melody played by the thumb. thats the easy one. Then you progress a bit, and I recall freight Train clawhammer style and Anji were the next area to master. yhen there was Doc Watson and flatpicking Black mountain Rag and Beaumont Rag. I kind of gave up around them, I can still only play them slowly. Kahandu I think mentioned earlier, you dont have to learn the whole piece, the first couple of bars does the trick. You just throw them in while tuning up/warming up, and people think you can play them. Stopping just shows how cool you are "I cant be bothetred to play something so corny and well known". The first part of Anji serves this purpose, forget about the second bit.
   Now the fanciest guitar piece I ever tried to learn was Dave laibman's finger-picked version of Orange Blossom Special. I got him to tape it for me played really really slowly so as I could learn it, and I've been tinkering about it with it for 40 years. The fact is, I am now coming to realise, is that learning that piece is like shagging Brigitte Bardot. It is not going to happen. And I'm not sure that I want to any more.