I don't know if this topic has been covered or not, I didn't search, but I thought maybe I'd show everyone what I do when a customer asks me what to do when they want to upgrade their P bass.
The first thing I do is take the bass and the body completely apart. Then, I clean out the body cavities with denatured alcohol. I then completely shield the cavities with shielding paint. Like so:
Notice that I purposely bring some paint up onto the surface of the body so that it will make contact with the sheilding tape on the pick guard.
While the body is drying, I get to work on the pick guard and tone circuit. I shield the area where the pickups go and I also make sure that the shield tape goes all the way to the aluminum shielding tape that comes from the factory. If it isn't there, use copper foil for that too.
Be careful, this stuff can cut you like a razor blade.
Then I get to work on installing new pots, tone cap and jack. I only use USA Vintage styl 250K pots with either a PIO, Orange drop or Chiclets style tone cap. On occasion I will use 500K pots if a customer would like a bit of a brighter tone.
Here are the pots in place ready to be wired. Notice that I have pre-tinned all of the lugs on the pots. Also, Squier used smaller 1/4" tone pots. I had to drill larger 3/8" holes in the pick guard for the larger posts. Easily done with a 3/8" drill bit and drill press or a steady hand and a cordless drill.
With those in place, I wire all of my bases with the same cloth covered vintage style wire. Here it is all wired up.
I like to use many different pickups. I don't have a favorite, but at the moment, I really like the products being put out by Tesla pickups. Check out these Phat 60's vintage style P bass pickups. They are built using high quality parts, with heavy gauge copper windings and vintage style cloth covered leads.
Once everything is wired, I re-assemble everything and check for hums, pops, etc. before re-installing the neck. BTW, check out the new control knobs.
This bass will not only sound better than the original Squier components but it will be much less susceptible to problems down the road.
Hope this was helpful.