First of all, don't make the mistake that you need to buy a Fender Jazz Bass because your favorite player plays such a bass. You don't play like Geddy Lee, and you never really will. You'll develop into your own player and you need to make up your mind as to what sounds good.
You have a Squier P Bass right now. The average Squier P Bass, IMO, sounds pretty good. You might end up having buyer's remorse if you just blindly buy a Jazz Bass without having some experience with one, as a P Bass is thicker and bigger sounding and easier to dial in a tone that works with a band. You can split the difference with a PJ Bass, because honestly, IMO, the sound of a Jazz Bass neck pickup is kind of like... it's good but I'd rather have a P. ANYWAY, WITH ALL THAT SAID...
Save up for a Fender. You could just as easily get a VM Jazz Bass for the price of a low end Fender on the used market, or in some cases, like Modern Player Fenders, you might even find a deal on a new one that lets you get a new Fender for the price of Squier. Some weekends at Guitar Center, they have trade-in specials or whatever where you trade in anything and you get 15% off.
And it's not about quality or sound because we all know that a VM Jazz can easily beat a Fender Jazz (not all Fenders are good) and sound is mostly about pickups and strings, and playability is mostly about hardware and setup. Especially if you end up with a Modern Player, they're Chinese made anyway. But it's about the sticker, and it's OK to admit it. You're 16. You're going to show up to a lot of gigs and practices and auditions in your life, and guess what, you might not care about the Squier decal that much, but others will, especially insecure fellow musicians in your age group. You're going to need at least one bass that can help you look the part as well as sound the part. Three years down the line, someone wants to shoot a music video. What would you rather be seen with a Fender or a Squier? See, you might not care, but others might, and your success in the music world often has to do more with how other people see you than how good you are.
Once you have at least one conventionally professional bass, then, I don't think it matters as much what your other basses are. I have a Fender that I'd show up to an audition with, but as soon as I got the gig, I'd not hesitate to break out my Squier or Ibanez. Make sense?