The paralell sound is the sound you already have, of each pickup wired separatately into the circut. The Series sound basically wires the two jazz pups into one big humbucker. In Series, the bridge volume pot is bypassed, and the neck volume controls both. The resulting sound is thicker and a bit louder, with a bit of bass boost and not quite so much high end. Series is often compared to a p-bass sound.
I wired my jazz with a Series/paralell switch and I love it. It's like having a whole different set of tones available for the price of a 13 dollar push-pull pot! I had a bit of difficulty following written instructions the first time I did it, but just this year SD put up a pictorial schematic for this mod.
http://www.seymourduncan.com/support...c=jass_bass_sp I used it a few weeks ago when I rebuilt my jazz, and it's dead simple to do.
As for what to change out. The Jack is probably fine. The pots may be worth changing, but I wouldn't bother unless you've played it for a while, and you are unhappy with the sound. I would recomend adding the push-pull pot for series paralell right away as it's gauranteed to give you more tonal options.
If you do end up changing the pots, get a high quality capacitor as well. I like the Sprague "Orange" caps, but theres alot of good brands out there.