I am very very likely to be getting a Basenji, but one thing still bothers me:
The neighbours next door got a Jack Russell, and I have no idea how this dog will react to a Basenji being introduced to his territory - or how my Basenji will tolerate a small little Jack Russell living in her building!
Any suggestions or advice on how I can take to make this work out as good as possible for everyone?
Many basenjis have dog friends. My girl Sophie loves my friend's Border Terrier and her Whippet. If they are well socialized it shouldn't be a problem. That goes for the JRT also, if it is well socialized with good communication skills it should not be a problem.
Will the dogs interact off leash or only on leash in passing?
I wouldnt worry too much, like Ivoss says Basenjis do like dog friends just like any other dog. When i moved into my partners house with my Basenji, he already had a large dog. The two got on realy well, however Benji did become the top dog despite it being Max territory and despite Max being 3 times as big 
My neighbors all have dogs and they all got along fine (except for one) with mine. The only one that didn't was a poodle-wannabe bitch that really was a "b i t c h" and hated any other dog she encountered. As long as the other dog is socialized and yours is too there shouldn't be a problem.
If you have a fenced area, these 2 dogs can wear each other out…I love to watch the b's run with other dogs.
Where are you getting your b from??
My brother has a jack russell and brings her over all the time and her and Abby play. Abby doesn't know that she's not a b. The only dogs Abby doesn't like are big dogs. 
Shaye gets along with most other dogs and plays well with all of them, big or small - she seems to enjoy playing with the big ones best, because when she jumps up with her front feet, she isn't coming down on the dog, so the other dog will play back - when she does that with the little dogs, they get a little defensive because I think to them it feels like a dominance move, even though Shaye is just playing. She does very well with JRT's though - they have the energy to run with her and keep up the antics. I believe well socialized dogs can all play well together regardless of their size.
My Bs are most gracious to other dogs. One of my Bs best friend is a 100# German Shep.
In our apartment complex, there were a lot of other dogs. There were 6 in our building and 8 in the building next door. We didn't have any problems. Cody marked a lot of territory, though. He did make friends with an older JRT that was deaf, but many of the other dogs were either aggressive or barked a lot, which scares him.
Now we live with Moe, my family's overly excited mix that thinks he's human. There was a lot of growling and displays of domintation in the beginning, but they quickly became great friends and partners in crime.
Our building has plenty of dogs. I'd estimate around 40 or so, which it seems condensed at times as it's a high rise building. So Kananga ends up making lots of friends. I think on my floor alone there are probably 4 or 5 dogs.
He has done very well with other dogs. He has a few that he's particularly fond of, while others he just doesn't show as much interest. I know of a couple that have gotten growly with him, although fortunately he never seems to react to it. I think he knows to just keep distance and not cause problems.
The important thing is being cautious around new dogs that the Basenji meets. Keep a firm tension on the leash in case the other dog decides to start growling. After that you can gauge the friendliness between other dogs and know which ones to be careful around.
My brindle boy has always been very kind with other dogs. Usually they approach each other and sniff things out. Every now and then he'll wrestle with a dog he knows, but that's not a common thing for him to do. I've never had him get aggressive with any dogs.
In all the years I've had Basenjis they got along fine with Jack Russells.
I stayed in a neighbourhood with plenty of dogs. My Bs are anti dogs. They are prone to aggressive behaviour because they want to be the Queen Bitches. I thought they were just anti JRT and Big dogs. Now it seems they are anti everybody….sigh......
