How old are your children? I believe, dachshunds are not generally recommended for small children but are okay with older children. I had one when I was younger too (not too fond now either).
Someone on the forum just got a boston/rat terrier mix. She could probably tell you about them compared to basenjis.
Visiting a breeder is definitely the way to go if you want to get a better feeling about basenjis. Good luck in your search!
I have 2 girls, ages 9 and 7, so they're well past the "squeeze it too tight" age, though I still wouldn't have them playing with the puppy unsupervised. I like the rat terriers, but I've just always been interested in basenjis. It's just so hard to get completely unbiased info, especially on the internet. From some of what I've been reading online, you almost feel like you aren't worthy of ANY breed, lol…