#1
I'm new to bass, and I just scored a Squier P-bass in decent shape on ebay for about $80.

I willing to spend another $100-120 to upgrade the bass a little. My instinct tells me that the first things to be replaced are the pickups, the pots, and the tuners. I can easily do that within the price constraints.

Is it really worth me replacing the pickups though? I know that your sound is a lot more about what you play through than your pickups. After reading the FAQs, I bought the Ashdown Perfect 10. so does it make sense to replaces the pups?

anything else i should think about changing on it?

thanks for your help.

Gear:
Partscaster/Tele into a bunch of pedals, a Maz 18 head, and a Z Best cab.
#2
You should upgrade the bridge, rather than some of the other stuff. It makes such a difference! Get a Badass II bridge.
Ibanez SR505
Ashdown ABM 300 EVO II
Epifani UL410
#3
IMO tuners are the last functional upgrade on a bass, it's not like a guitar where you are constantly pulling the strings out of tune with a whammy or trem bar. Also (despite the discerning ears of actual bass players) listeners can't tell if a bass guitar frequency is a few cents off as they can with higher pitched guitar frequencies, so if it goes a tiny bit out of tune while you're playing, it's not often a real big deal.

The upgrade depends on what you want to change: a new bridge=more sustain, new pups and electronics=a different tone.

If the pups are noise you might just wax pot them for less than $10, there is a tutorial you can search for. Changing pups will change your tone a lot, but if you just started, I don't know why you'd want to make changes. Try playing for a few months before you upgrade, suppose after 3 months of playing you really want a jazz bass sound? now your $70 p-bass pickup was a total waste.