I would actually recommend the Squier Modified Jazz Bass...I love the feel and range of different that you can get with that bass. And it's got decent pickups in it already. Just a suggestion.
I'm not too sure about the pickups, I've never tried them.. However, I do have a Badass Bridge on my Fender PBass and let me tell you, it's the best thing I've ever had, it makes the bass feel so amazing. The strings feel loose and smooth with is great for soloing and the sustain is fantastic. You can't go wrong with the Badass