I think you are doing the right thing trying to find something to keep your interest rather than just flat out giving up. Yes, having complete songs that you like which suit your playing level makes a big difference. You have to have fun!

One question - have you gone through any of the branches in the core system? After the first 2 parts, you can choose blues, rock, or country. I'm currently going through the blues one and I think it's great. I can remember going through similar stuff back when I was first learning. Even if you haven't completely mastered the first 2 parts, you could start with some of that.

Many of the songs I learned at first which were cool and relatively easy to play were Beatles and Eagles songs. GT has great resources here, but don't limit yourself to only songs here. I have a music book of all of the Eagles songs and it's great fun to pull that out, cue up Eagles Greatest Hits, and play along.

Lyin' Eyes is a great song to strum too. So is Best of My Love. Something from Abbey Road is another one I had learned. It also has a relatively easy, but cool, solo. Day Tripper has a cool guitar riff and relatively easy chords. Hotel California is good - you don't have to learn the exact finger picking parts and stuff...learn the chords and strum along. If you are starting out, just being able to do that is an acomplishment and can give you lots of enjoyment. The Rolling Stones have some easy stuff too, or at least can be played in an easy way.

Don't let your dislike for some artists turn you away. Learning to play a song that fits your ability but perhaps isn't your taste can give you a new appreciation for the song. I was never much of a Rolling Stones fan, but it was fun to play some of their songs.

I agree that just doing exercises can get boring and you feel like you get nothing out of it. I found that practicing scales helped my dexterity and finger strength. I also plan to do it to help train my ear and learn the notes on the fretboard. Do stuff like that, but mix it in with fun stuff.

I hope you find something to keep your interest.