We had a JRT, Sherman. Although frequently he was referred to as Shermonster. His favorite thing was sniffing out cash money and eating it. We learned pretty quick not to leave bills in a pants pocket and then throw them on a chair or the bed, or to leave an opened purse anywhere he could get to it. Went almost 18 years without a dog after he departed, sadly. Shortly after house arrest started, we adopted another JRT, Baxter. He's integrated well in to the family, but he's still a JRT.
They have boundless energy. They're incredibly smart, and easily trained if you know how. If you don't constantly maintain your position as head of the pack, the JRT will take over in a heartbeat. As in, the second you slip and let him think he's calling the shots you have a problem. Did I mention they have boundless energy? Plan on a couple of long walks each day or they get restless and find ways to let you know they need an outlet for that energy. Fenced yard is a really good idea. They're generally gregarious and enjoy meeting new people (sometimes they enjoy this a little too much) and other dogs. They typically will form a primary bond with one member of the family, which is interesting, but that doesn't mean they ignore or avoid everyone else. Quite the opposite, but that person they bond to will never get a moments peace. Sorry, hon, he picked you!
Beyond all of that, they're still a terrier and do what terriers have been bred to do. Baxter has killed more backyard rabbits and squirrels in the last two years than I care to recount. It upsets my wife, especially when he comes to the door all proud of his trophy, his mouth and fur bloody; but that's what they were bred to do. On the other hand, when the neighborhood deer herd comes around every night to eat the landscaping, he somehow knows (even if he's asleep) and loves going out there to terrorize them until they leave. The hostas actually got big and bushy this year! We know as soon as the Amazon van parks at the curb, someone pulls in the drive, or the postman is next door; great little warning system.
Jacks are fantastic companions, but you need to understand what you're getting in to. It's not a fluffy little poofball of a dog that will sit idly all day just waiting for a chance to go to bed and snuggle up. Active is a tremendous understatement, but hyperactive carries some negative connotations that I don't think really apply. We've had mutts, schnauzers, a minpin, cats, and now two JRTs. Wouldn't pick any other breed, but we know how they operate and enjoy what they bring to the table (unless it's a mangled rabbit or squirrel).