Strings are a matter of preference. The stock strings will probably be okay, but not great. If you're into Pete Wentz's tone, go for roundwounds, not flat.
The pickup is a Quarter Pounder, which is a great P pickup. A lot of people upgrade their Squiers with that pickup, so no mods are necessary. If you want something more vintage, I'd suggest getting a different bass rather than swapping out the QP since that's really the strong point of the Wentz sig.
I'm not sure what pots Squiers use, but 250k CTS pots will probably be better than whatever is in there. Since the Pete Wentz sig only has a volume pot, this is a really cheap upgrade.
Shielding the pickup and control cavities is always a good idea.
The stock bridge could be better. Some good drop in replacements are the Gotoh 201 and Bad Ass II. Both should increase sustain a little and be all around sturdier, and the Bad Ass will probably add some more treble bite. The Gotoh is much cheaper though.
I would replace the stock nut with a Tusq nut if I were being anal about it, but the stock one should be fine.