If you know your dogs are good at the dog park, then that is probably a good place to introduce them. I would first let them get rid of some energy there before the puppy arrives, and then allow them to be in the same area.
You shouldn't force them to interact, so it would be wise to continue playing with the JRTs as if the puppy wasn't there. This will help them see the newcomer as not a big deal, and they will just get used to each others' presence in a gradual way. After a few minutes of this, stop playing and see if they interact. Be sure to redirect them if you sense tension from the JRTs (so you would invite them to play with toys, or just to follow you).
After that goes well, you can take them all on a walk together in the park so they get used to walking together. Being outside is much less stressful for dogs who are first meeting each other, since they are not confined to the rooms of a house. Since the walk will start with all of you together, you shouldn't have to worry about them barking at each other.
When you get home after all of this, allow the puppy to walk in the house first. I am honestly not sure why, but the behaviorist that I have learned alot from told me that it is best to do it that way.
I hope this helps! All of your new dogs should be nice and tired by the time they get home, and they were doing something fun together which will make a good first impression.
And I have one more piece of advice! I would contact a local "positive" trainer to help with the barking while on walks. Your new pup is most likely going to get this new habit from the JRTs, and it is both annoying to whoever walks them, but it is based on an unresolved feeling that your dogs have towards strange people and dogs. Training will both solve the problem and it should also resolve that feeling that they get when people and dogs pass by. So in other words, they won't think "hey that person is offensive and scary, I am going to bark until they go away...hey it works!" to "this strange person is ok to be around. i dont feel the need to bark at them anymore."
Hope this helps!