Since you frowned and I get to see my new avatar i'll give it a go. For playing by yourself I would go with the following:
Ramble on Rose, check out Jdarks for loads of riffs. Great chord progression with tons licks that follow the chord pattern.
Terrapin (ending part after they sing Terrapin!)
Brown Eyed Woman
Deep Elem Blues
Learn to fingerpick and no better way then playing Gary Davis/Jorma tunes at:
Death dont have no mercy
I know you rider
That will never happen no more
Key to the highway
Thrill is gone
Honkey Tonk Woman
Dear Mr. Fantasy
Over the hills and far away
I would pick any tune from the above and check out utube for videos and the net for tabs and listen to it and play. They are all tunes that sound good with one person playing with or without singing.
Utube is a great place to learn techniques, check out ebicks and jdarks stuff. Much easier to pick up new things by video opposed to reading a tab.
I'm not one for finger training and memorizing a bunch of scales. I find it tedious and no fun. I can go to work if I want that. I do highly recommend learning the caged system for being able to play leads and chords all over the neck as it open up a lot of possibilities to change and add to tunes.
Hope this helps