You would prefer passive pickups, the actives(which had that 9V battery) are less versatile in the range of timbres(the sound envelope is the same), they tend to be repetitive in the timbre range they provide.
I agree with this, but most good modern bass guitars that use 9V batteries (I have one that uses 2!) are for the electronics (2- and 3-band eq, etc.), not for the pickups. And most have defeat switches on board to bypass the eq. Other than EMG, no manufacturer makes actives exclusively for bass.
As to woods and hollow, semi-hollow, solid, etc., it all depends on the tone you're looking for. No one instrument will give you everything.
As to a starter bass, the MIM Fender is good. I'd also consider Ibanez.