I am starting all over again, myself.
When I learned for the first time, I was fourteen years old, and I knew so little about music. The teacher I started with got me playing some very basic riffs. Popvana's Smells Like Teen Spirit, the main riff basically consisted of a series of four notes repeated four times a piece. Playing that bore at least taught me to move my hands around the frets and to pay attention to the note to note rhythm.
But I really started learning when I got a good teacher and he taught me the bass parts of Black Sabbath songs. I think the first song he taught me was Symptom Of The Universe, which has some very good riffs for learning.
I also highly recommend finding tabs of songs that you really like. It is no good learning something that you despise the maker of. When I learned what Popvana or more recent era Poptallica songs consisted of in bass terms, it did not take me long to stop listening. Whereas learning the bass parts of My Dying Bride, Black Sabbath, or Mr. Bungle songs furthered my appreciation of them.
The challenge I am facing right now is finding songs that have riffs within them that are simple enough for me to keep playing over and over to get my hands back in shape, but will keep me interested once I get past that. A lot of the songs I really want to learn are not on this site, but I will keep wishing. Right now, my way of thinking is that I will practice the individual bars of David Bowie songs like Station To Station, and then start stitching the bars together until I can play big parts of the song.
This is just my opinion based on how I learned the first time around, of course. But one thing I must stress above all else is, if you are not enjoying something, stop it. Do not stop playing, but stop the exercise and try to find something that works for you and accomplishes the same end. For example, if you are not enjoying playing Poptallica, get a tab of the bass intro from My Dying Bride's Gather Me Up Forever, and play that instead. I did more or less exactly that.
And always remember. Music should be fun. Even the pros know it on some level. If you are not having fun playing, the people watching you are going to pick up on it.
Now please excuse me whilst I play the hammer-on opening bars from Station To Station for about six hours.