Congrats! Post some pics of your new bass when you can. I've installed EMG Geezer Butler passive pickups on several P-bass copies. They're easy to install and sound great to my ears. GZR P I'd leave the bridge alone. A high-mass bridge will give you a bit more sustain, but the bent-metal "vintage" bridge works fine and is more in line with the traditional P-bass performance.
Along with the above-mentioned pick up options. May I suggest just playing it for a while stock. You maybe happily surprised.
Absolutely. Most of the Squier precision pickups I've encountered sound just fine and they don't hum.
I have changed pickups in P basses, not because of need but because I wanted a specific sound, like aggressive Model P pu. Or a little less output vintage sounding 62 pu. But as I noticed they didn't change the inherent sound of the P bass, it still sounded like a P and maybe the differences I heard, I was the only one hearing. Anyway, carry on!
woohoo! Great choice. Personally I’ve been pretty happy with Squier pickups, and strings seem to make a bigger impact than pickup swaps. That said, I have a Duncan SPB1 in my main bass and I stopped looking at pickups after I got it. Great pickup, highly recommended!
String choice will likely make the biggest impact on tone. Consider that before pickups and bridge. That said, I did all 3 on my 2000 Fender P and I think it’s become a much better instrument for it (GHS Boomers, Fender VMod pickup and KickAss bridge). I have EMG Geezers in my “Mutt” and think they are quite good too.