Learning scales is essential. It's not that you'll necessarily be running up and down scales on a gig, but that knowing them gives you much more familiarity moving around the fretboard and helps you learn by ear - you start developing a sense of where the song is going, what that note you're hearing on a recording probably is or isn't. Practicing doing them faster and faster can help your technique as you start having to tame flying fingers and work on being precise and controlled. You can also get the exercises from the book Bass Fitness by Joaquin des Pres, just the first few pages made me a much better player.
Train your ear by setting tabs aside and figuring out songs without them.
What songs to learn is totally up to you. I would say divide your practice time (which should be every day, or nearly so) between exercises and scales and such, and learning songs. It's good to have a repertoire and songs are more fun than exercises, so they keep you motivated and excited to be playing. You may have a genre you want to be in a band playing, so build your list in that direction, or if not I would say look at things like the DJs' list of most-requested songs, that's always a good place to go for what you'll most commonly be asked to play in generic situations. You may also pick some bass heroes (McCartney, Squire, Duck Dunn, Jamerson, whoever) and start looking at their lines - it's amazing where they go sometimes.
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