For volume and tone: you can use Audio or Linear taper, but note that Audio taper is used more often on a regular basis on most wirings, that means, it's a safe option, so it is the taper Value, 250Kohm is the standard as well and should be fine, unless you have enought time to order different values and try them out one by one (it will depend mostly on personal tastes) Note that different values will make the "volume sweep" faster or shorter, even sometimes, so fast that will be kind of like an "on-off switch", So:
25K: Value used on active basses (active pickups or with the volume a tone controls placed after the preamp).
100K: Will sound too dark, softer volume sweel and less output.
250K: Standard, it will work and perform fine, specially on Audio taper, some people say that's the most usefull range.
500K: Brighter and a bit more output, but if you use Audio taper, the volume sweep will be slightly more abrupt, so some people use Linear taper to tame that.
1Meg: Even brighter and a bit more abrupt than 500K, also a bit more output.
(Be sure the Tone pot is audio taper).
There's some missundertunding about wich value to choose on P-basses because the pickups are called sometimes as "humbuckers", and they are but the construction are very different from a typical guitar humbucker pickup, that needs 500K to perform well because you have 2 complete coils on them, (this is a quite complext to explain), but the P-bass pickup is technically a split-coil, even having that humbucker effect, the coil lenght is just slightly longer than on a J-bass, so 250K will perform better.
Then, the Cap Value: Higher the value of the cap, lower the cut-off frequency, (and darker the sound when messing with the tone), also note that the instrument have an usefull filtering range (right before it gets too muddy to be mainly usefull), that's why the value is different for each type of pickups that use different pot values, just to keep balanced that usefull range, so:
.022uF: Commonly used on 2 complete coil humbucker (with 500K pots) for a most usefull range. if you use it with standar P or J pickups (250K pots), the it won't cut as highs as desired.
.047uF: It will work as desired on P or J pickups (250K pots), on typical 2 complete coil humbucker, it will cut even more highs, getting muddier.
.1uF: Commonly used on active pickups (and/or with the preamp placed before the V/T controls), on standard P/J pickups will get muddier, but with 2 complete coil humbucers, the sound can get even more muddier that using .047uF.
So, normally you will see:
.022uF with 500K (humbuckers, specially on Gibson Basses).
.047uF with 250K (single coil, split coil, but sometimes on G&L and Musicman humbuckers).
.1uF with 25K (actives).
So, unless you have enought time to try several values in order to find what you trully like, keep it basic and simple (all of this is kind of a rabbit hole! hahaha), also for the tone cap type, you can use mylar or ceramic, it will be fine, but even the fanciest and most expensive cap on the market will make just a small, tiny, negligigle difference, so paying 20 bucks for a "posh cap" is not worth it.
So the last thing to mention is the Potentiometer brand, both CTS, Bourns and Alpha (taiwan) are very reliable quality-wise, the only thing is that Bourns use to have normally a super-soft turn, CTS use to be a bit harder than Bourns, and Alpha, somewhere in between.