EMG requires a 25K, Seymour Duncan requires a 125K and some others require a 50K pot. A 250K will work (as in produce audible sound) but your pickups will sound very poor. EMG pickups already sound shrill but a 250 or 500K pot would make them sound broken.
As for the jack, it’s necessary for switching the pickup on. If you leave your jack plugged into the guitar 24/7 your battery will drain quickly. That’s why you have to unplug the guitar when you are finished with it. It connects the pickup to the battery. Last I heard, that means it’s basically used as an on switch!
Sorry to save but most Guitar Center Guitar techs and in a lot of cases, your mom and pop places aren’t really up on active electronics. In fact, I have three places in my area and none of them will install actives.
The pots that come with EMG are great. The ones that come with Seymour Duncan are utter crap in my opinion. However, you can cure a lot of the shrill EMG tone with getting a few Drop Orange caps and chucking the caps that come with the EMG. The drop Orange have a better overall tonal sweep and will help give back a little natural sound to your guitar. They go into every active guitar I do and just about every passive one too.