Welcome, Brother Sharkbait!
Sharkbait Ooh Ah Ah!!
I'll say right off the bat, I am biased when it comest to suggesting basses, but in this case I can think of some valid reasons to back it up. My first bass was a used Fender Aerodyne and I still love it to pieces. Despite not knowing much of the ins-and-outs of bass guitars (I won't say "at the time" since I'm still learning soooooo much), I stumbled onto a d@mn good find.
If you're coming off an Ibanez, I'm guessing you'd prefer a lighter body with a very slim neck. The Aerodyne has a Jazz neck (1.5" at the nut) but a tighter radius than most (7.25" vs. 9.5"). Also, mine weighs in at 8.5 pounds which is significantly lighter than your standard Jazz bass.
As far as tone goes, it's plenty deep enough, but can get more aggressive with the mid-tones when you start adding in the Jazz pickup. It's not a cannon like my Blacktop Jazz, but I don't think one of those would be right for the musical genres you mentioned.
One other thing I almost forgot to bring up…
…it's a sleek and sexy as all get-out!
Usually they go for about $800, but right now Fender is doing a big summer sale. The current retail price is $750, but I'm sure you could find a used one for significantly less, just like I did.