Get what you like the most. In Jazz, many will say it doesn't matter, but every band leader or group is looking for a certain sound or thing. Playing ability to me is more key in Jazz and even other genre, in Blues it don't matter, if you can keep a 12 bar blues, good sound etc. you can show up with an Alex Webster sig spector! If you go to a Jazz Academy chances are you will learn Upright bass most likely, which is a great thing but I have no idea where you are looking.
Fretless is great, but personally I save that for when you get to your school, you can get a close tone to an Upright there is are a load of guides on here so I don't wanna repeat.
Biggest thing to me personally for a bass in jazz, it's nice to have a control of tone and I am going to be devils' advocate and say look into something like a Yamaha, something that has a solid tone and lots of controls like a TRBX or even BB.
BUT that is what I would go with, G&L, Sire etc also have loads of controls, and I think you should choose what works for you, I also am unsure but if you do not have a performing rig, amp, amp head or decent combo etc. I would honestly look into that more if you have Sandberg money, with a Cort you can go far, but you can't go far on a low watt combo that isn't quality. I know in college its provided, and I do not study music but you see it and hear it all the time being in the music world and jam world that someone will have to buy their lent instrument or lent amp and now they are ampless or instrument-less. Also do not feel upset or threaten by those with better gear, a lot of upper-class rich kids went to my HS and had the new everything, doesn't at all equal skill better gear. A famous saying in fishing world - "This simply feather lure can catch every bass you need on a fly, and this simple little fly lure can lure in trout of all sizes!" , a salesman said, then a young college beginner asked "What are those pricey colorful lures for then?" the salesman said "Those aren't for fish, they are for luring fishermans cash!"

(Forgive it's such a dumb thing but I love using it in all hobbies that story LOL)
Anyway it's a choice you have to feel and find, we can only guide you. Many on here will push for the classic Fenders etc, but do not let the crowd make your choice, just guide. I would choose totally different things but at the same time I think you have to feel what is best. Also I think going into a Sandberg, while they are amazing basses may not be the best IMO for something like jazz, (I know eating my own worlds saying anything can work in jazz) if you want a near close but not identical sound a lot of jazz cats, I seen a Rob Allen used a lot but they are pricey and something I personally say is post-grad level.
This is all just my opinion. Good luck in your search and studies. Forgive my ramble. Thank you again!