A jazz will do the job in almost every genre.. Squier or SX basses are a great bang for the buck. The Squier VM and CV are awesome if you're looking to play something right out of the box..
I picked up an SX jazz from soft recently which was in appalling shape, looked as if someone picked it out of the rubbish dump, seriously! It had dust and dirt all over, fingerprints, rusts.. If I was presented this bass claiming it's from the 60's I'd have believed whoever. The pickguard was off and the rout job was horrible, I took a peep into the pickup cavities prepared for the worse, it was absolutely gruesome! There was shit, gum, sticky wood stuff.. Looked like huge figs grew in there. Secondly, the neck heel and cavity were poorly measured. The heel was too flat and the cavity was over sanded down hence the strings were flying above the fingerboard like a UFO
Anyway, long story short.. Cleared the horrid mess in the cavity, wiped the bass down, polished it, cleaned the frets and oiled the fingerboard, replaced the bridge, decided on a quick self fix for the neck and threw a neck plate I had lying around in between the body and neck, PERFECT! Then gave it a good setup and threw a new set of strings on.. WOW! It's just about the sweetest jazz you'll ever play.. Neck's perfectly fast and comfortable, tone's definitely a killer and to top the whole thing off, it's got tons of MOJO!
I took it ahead of my 1000x more costly basses to countless gigs and recordings thus far. Really love it.. The fact that I can trash it around and it still produces the "OOHLALA" gives me great satisfaction!
Might throw in a different set of pickups and a preamp someday, but for now.. THIS IS 'IT'!
Moral of the story, Fender's or pricey basses are not always the most enjoyable