I see it's your first day as a member. Welcome to talkbass, the website that will eventually destroy your playing until you descend into madness. (It's not that bad

)
You had some pretty god answers already, so I'll give my own version of what you should be concerned about as a beginner. The rest will come as you get more experienced.
1- Bass models.
Bass models are endless, and they all have certain companies. (Fender, Rickenbacker, Music Man, being some of the more popular). Bassically, models count more or less by the type of pickup they use (The blocks under the strings).
Precision bass:
Jazz Bass:
Rickenbacker:
Stingray:
Pickups (PU):
Precision bass uses split-coil pickup, which look like this:
Jazz basses use two single-coil pickups. Each pickup has it's own volume knob, used to change the tone. Pickups closer to the bridge will have more treble and less bass. Pickups closer to the neck will have more bass.
Single coil PU:
Humbucking means hum-cancelling. It uses a negative hum and positive hum that cancel each other out, eliminating noise.:

(this shape might also be called soapbar)
You'll see variations of these, but for now, that's all you need to know.
The bass you use uses two humbucking pickups.
Active and passive:
Active basses use a 9 volt battery to power certain controls. Active basses make less noise, have greater tonal options than passive basses. Bottom line is: Active basses and boost and cut EQs, whilst passive can only cut.
Strings:
Strings affect quite a lot the tone of the bass. There are two major types: Flatround and Roundwound.
Roundwounds are used more commonly, in any genre. They are good for all purposes.
Flatrounds give a smoother sound and feel, and they last longer. But they are mostly used for jazz.
You can bet a bass with either 4, 5 or 6 strings, 4 being the most common. I personally prefer 5, but that's just me.
I would recommend you start with nickel roundwounds for now.
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Every bass sounds different. Go to youtube, listen to different types of basses, learn what you like. Practice and you'll learn all you need to know.
Congratulations, good luck, have fun and God bless.