Hi Tyran,
If you can anyway afford it, it really would make sense to get a couple of lessons from a teacher, just to get the basics in place. Bad technique can, in a worst case scenario, actually damage your wrists, so it's important to get it right from the start, and the best way to do that is see a teacher.
As for things to practice, a lot depends on what you want to play. Working with tab stuff is a good way of getting started on playing tunes straight away, but you might have as much fun finding chord progressions on the net and just playing the root notes in time with a drum machine, metronome or the CD. Then as you learn more theory, you can add other notes.
Pick a bassline that you know so well in your head that you can sing it and try working it out, one note at a time. Use the pause button on the CD player! :o)
Rickbass's suggestions sound fun, though using three fingers on your right hand isn't neccesary. If that works for you then great, but two is generally easier, and won't limit you in what you are able to do. if you feel like adding a third finger at some later date, that will probably be easier than struggling with three at this stage...
If your hands start to hurt when you're pracising, stop! Don't play through the pain barrier, take a break, flex your hands, get a drink and then come back to it. If a stretch feels really hard, try pivoting your hand rather than over-stretching your hand.
Oh, and as soon as you can, get playing with other musicians - find a guitarist who's learning and get together to jam and have fun!
Good luck - bass is a great instrument, and I'm sure you'll have great fun,
cheers
Steve
http://www.steve-lawson.co.uk 
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