I've grown up with JRT's and can safely say that no two are alike...
Please don't be fooled into thinking that they are a small dog. Any JRT owner will tell you that they are anything but.
They are a working breed that was 'designed' to kill rats and go down rabbit holes.
They are brilliant, intelligent dogs that can be loving, loyal, fantastic companions. They are also stroppy, arrogant little shits that only walk sideways at the end of the lead, will only start 'discussions' with ferocious dogs at least four times their size, chase cats, chew stuff.
They'll do as they're told as long as they think it was their idea. 
If you are getting a puppy then you need to meet both mum and dad. However, their temperament is no guarantee and you will get very different personalities from litter brothers and sisters.
Can you spend some time at somewhere like a local Dogs Trust so that you can meet some different breeds to see which would suit you? They may be able to give you some ideas about breeds that will suit your family.
This thread has made me remember just how much I bloody love JRT's... one day I'll have another one 