@buldog5151bass has the right of it, but I'll go a little deeper since it's a nearly infinite rabbit hole and you don't want to try to explore the whole space right away. You could change your strings once a week and it'd still take years to explore all the possible options.
This is because there are many dimensions on which strings differ. First is what kind of string (round, flat, etc.) and the second is gauge. I think you should start with those.
Kind is more or less a trade-off between brightness in sound and smoothness in finger feel. At the rough but bright end, you have rounds. Then pressurewounds, then half-rounds, then flats at the less bright but more smooth end. There's also tapewounds, which are also generally toward the flats end of the spectrum.
I'd settle on this first. Some people like the more zingy sound of rounds, some like the more thumpy sound of flats, some are in between. It sometimes depends on the bass, too. I have pressurewounds on my P and my J, rounds on my Rays (stainless steel on the short scale) and my HH Sire, and flats on my fretless J (for now).
Your Ibanez is coming with standard nickel-plated rounds. If you like the sound and feel of those, great—keeps your life simple. Pretty much everyone who makes bass strings makes rounds and they're generally the cheapest. If you think they are too rough-feeling or too bright, then try something else, and beware of how many options there are.
Then there's gauge. Since you play guitar, you probably understand the tradeoffs there: heavier gauge lets you dig in more and gives more sustain, lighter gauge means less effort to fret/bend, etc. 45-105 is the most common set for 4-string basses and if you don't know what's on your jazz bass, it's probably 45-105s.
If you want less tension so fretting and bending are more guitar-like, get lighter strings. If you want to dig in more or your strings feel floppy, get heavier strings. If what's on your basses is working for you, great—again, that's one less thing to worry about.
The other issue with string gauge is whether you care about having the same tension from string to string. Most sets have higher tension on the A and D strings. My take is that this doesn't bother most people. If you are in the "don't care" crowd, once again, great—it simplifies things; just get whatever has the appropriate weight for you on the heaviest string and be done with it.
Side note: I think most people don't care because what seems to be the most common size strings is 45-65-85-105, which is not balanced; there's about 25% more tension on the D than the E. I know it may look balanced, but to maintain balance the difference between gauges needs to increase between each string, not be the same. 45-60-80-105 would actually be more balanced (E is still a little low there); D'Addario makes a "balanced tension" 45-60-80-107 set. I tried this for giggles once and it ruined me because I really liked it, so now I try to find balanced sets. Finding a well-balanced set for a 5-string is not easy. I finally just gave up and got a Stringjoy custom set and I think I'm done looking. End side note.
And you're right, stuff like materials and core shape matter as well. If you want even brighter and even more rough to the touch than regular rounds, get stainless steel rounds. Then there's stuff like pure nickel, cobalt, etc. for even more variation. And core shape, too—hex is stiffer. I wouldn't start messing with this stuff right away, though, focus on kind and gauge first.
TLDR: If you like the standard rounds that come on the Ibanez, great. Stick to rounds of "standard" gauge and keep your life simple. If not, welcome down the rabbit hole.
