Ilindy -- I can tell you just about everything you want to know about Basenjis (or don't want to know, as the case may be!). They are a wonderful breed, in my humble opinion, and I likely won't ever own anything else. Non-barking (a plus to me), manageable shedding, no odor are their claims to fame (I always say if I didn't have to feed them and clean up poo they'd be the perfect dog). HOWEVER -- that being said, if you're looking for a dog that will cater to your every whim, fetch your slippers, drop the newspaper at your feet, and maybe bring you a beer, keep looking. Basenjis, while very intelligent, are not necessarily easy to train. They are usually quite independent and think for themselves (qualities that are highly prized in their native Africa, where they are used as hunting dogs). They are in the hound group so they usually have a very high prey drive. The key to training them is making them think that what you want them to do is what THEY want to do. Of course, as with any breed, traits and personalities vary from individual to individual, and how they were raised by the breeder plays a role as well. Our male was raised by a breeder who socializes her dogs starting when they are puppies (and he's a retired show dog, so he's used to being handled), so he's very used to people and thinks everybody is his friend. We adopted our female when she was six. She spent the first five years of her life with a family who kept her crated a large share of the time, and being pestered by their young son. Hence, she's a bit more leery of strangers and isn't too fond of little kids. She won't go after them, she'd rather just stay out of their way.
Anyhow...rather than get into a long novel, I'll refer you to the Basenji Rescue and Transport web site if you want to find out some more.
http://www.basenjirescue.org/
Or, feel free to contact me via phone (or I can contact you) if you'd like.
Whatever breed you pick, good luck and enjoy your new "kid"!