Beta described very well the various Ibanez series, so I won't do it again. I'll just say this:
1. the higher the number, the better; you might think the differences between the models are minimal, judging by the specs, but trust me, they do sound very different.
2. you should ask yourself what type of bass do you need: you like a more "classic" (Fender type) tone, or a modern one? You like a thin neck, or a wider one? There are options, but only if you know what you're looking for.
3. try to test the bass in similar conditions as if jamming in the rehearsal room or on stage (for instance get your amp to the store - some basses sound differently on different amps; also, many basses sound different when played at home practice volume, as opposed to loud band rehearsal volume - in those conditions some tend to fade out in the mix)
4. as other said: SR is the Ibanez flagship, so it's prolly the safest choice; all the models of the line sound good, modern tone & looks, very thin & fast neck. SRX is the more "metal" version (or the Ibanez version of a MM) - but they have a specific tone which might not work for you (I don't like 'em, but that's a different story). EDB is my current choice - they feature the same quality as the SRs, but the tone is slightly different (the 550 has a very warm bright tone, while the 700 has a darker bassy tone and has the fastest neck I've ever played!). These two series feature high quality components that are hard to find in other basses in the same price range.
GSR is a very good starter bass, but other than that, I'd go for something different. BTB go in that "love it or hate it" category - many people like 'em, I hated my ex BTB (it felt bulky, the neck was way to wide for my liking, the bridge made intonation impossible; it felt like a piece of plywood - but it was the cheapest model, so...). However they do have a distinct sound and I can see why many people play 'em.
I owned SR, EDB, GSR, BTB. My opinion is based on my firsthand experience with those models, plus several other tested in the local Ibanez dealer's shop. As a conclusion: your choice depends on what type of bass & tone you like, the type of music you play and the gear you use. For instance, I loved my SR500's tone, but it simply couldn't fit in my band's sound, so I had to let it go; the BTB made us sound very "death metal" (which we don't play) so I had to let it go too. After 2 years of experiments, I finally decided to stick to EDBs, because to me and to my band those basses sounded the best FOR OUR MUSIC. In you case, it may very well be something else
Good luck!