For a beginner there are two basic bass "sounds". There's the Fender Precision (aka P-Bass) and Jazz basses (J-Bass). The P bass has a "slightly" bigger/thicker neck and a "mellower" sound while the J-Bass has a smaller/thinner neck and a bit more aggressive sound. By aggressive, don't think "heavy metal distortion" as those sounds are due to effects.
Fender makes the entry P/J basses in Mexico (Made In Mexico, aka the MIM-P and MIM-J). They're good quality, inexpensive and a great place to start your career. Also, you're guaranteed to find them at your local guitar shop.
Here's what I did, I personally knew nobody that played bass or guitar, so I went down to a local independent guitar shop that sold basses (not Guitar Center), and found a salesman and explained exactly what I wanted to do, "I want to learn to play the bass, and am interested in the P & J MIM basses." I asked the salesguy to play two of the basses (one P and one J) playing simple scales, I didn't want to hear how good this guy could play, but just wanted to hear what the two basses sounded like. I personally liked the sound of the P-bass, and then he showed me how to hold it so I could get a feel for comparing the neck of the P vs J. I have small hands and it didn't make much of a difference to me.
Instead of buying one of the "starter packs" I built my own for less $$: I took my MIM P-bass and bought a entry level practice amp (Peavy something...). This is pretty much what is in the starter packs (an entry level bass and a practice amp). I got a 15' cable and a soft gigbag (a bag for your bass with a pouch you can put some sheet music and other small items).
Lastly, I had the salesguy set up the bass for me (strings 'not too high, not too low') as I needed somewhere to start. Down the road, you'll determine if you like higher or lower string height.
One other thing: Get lessons. If the shop is good they'll be able to recommend a couple of teachers (or there are teachers associated with the shop). Find a teacher that plays bass as their primary instrument and hopefully has similar interests in music to you. On your first lesson, bring a list of songs that you want to be able to play. Even something easy like Queen's "Another one bites the dust" or Pink Floyd's Money are good places to start. The more you help your teacher, the more he/she can help you.
Lastly: Be patient, practice and have fun.