Hi! Hopefully I will be able to shed some light on what life with a Basenji is like. I grew up with labs and goldens, and while they're great, loyal dogs, they're (forgive me) more than a little dumb. I've always been a 50/50 cat/dog person, so when I began researching Basenjis, I realized I had just found the best of both worlds. Besides the fetch part that I was accustomed to with my retrievers, of course. My Penny's idea of fetch is: "I will thrash this stuffed toy while you watch it explode all over your floor… and run away when you get close. You shall not have it. You shall not pick up the fluff, either. That is for shredding when I'm done with this part." and... "Get that rubber ball away from me; it has no squeaker and I cannot thrash and destuff it."
So, my foremost piece of advice: If you do not have a sense of humor for antics and mischief, a Basenji will make you very unhappy. It's much better to laugh, repair what damage you can, and move on. My husband doesn't deal as well with this concept as I do, as he thinks "the dog is smart and should know better". The problem with Basenjis is that while they're smart enough to know better, they make a conscious choice to do it anyway. A prime example for me was the day Penny realized she could squeeze out of her crate if the bottom latch was undone. She then proceeded to attempt to burrow her way through the carpet and wall into the garage. She got through about 6 square feet of carpet by the time I made it home. I wasn't happy, but by being careless with the latch, I had really set myself up for it.
As a Basenji owner, you'll have to be able to outsmart a very devious, at times devilish, creature. You can certainly set yourself up for success if you know what you're looking for. I can give you a brief list from my experience.
- Papers left out and about will be shredded for you when you return to them. (This can sometimes be useful, admittedly.)
- Open doors = life is a highway, and that Basenji will ride it all night long before it looks back and/or misses you. Fear of cars, by the way, is nonexistent.
- Always open the blinds before you walk out the door to get the mail, or they will be ruined by the time you get back. Yep, it only takes 30 seconds.
- Anything wetter than dry grass is "wet grass". Wet grass (and rain of any intensity) has caused many a Basenji owner a soiled carpet and unapologetic attitude on behalf of their Basenji. Penny is one of the few I know of who has learned to do her business as quickly as possible to get back inside. I'm serious, she's fast. She comes sprinting in the house practically still in the middle of a bowel movement some days.
- A Basenji that is not crated is a ticking time bomb. They are most adept at identifying things that smell like you and ruining them while you're away, even if you think your house is spotless. Pants (just the crotch), underwear, shoes, retainers (that was an expensive one)... all consumed without remorse. I've heard of some people who have success with leaving their Basenji uncrated, but those folks are few and far between. It is much safer for the dog and your possessions if they are secured in a designated "den".
- Trash cans are too tempting, whether filled with paper or leftovers. They should have lids or be put away when you're not able to supervise.
- Basenjis are sled dogs, you are the sled. I've never met one that doesn't put most of its weight into the leash, especially when excited. It takes a lot of effort to leash-train a Basenji, as they're really inquisitive and want to sniff everything, even if it means leaving you behind. I certainly recommend a good harness, as Penny would hurt herself on a normal collar/leash combo.
While Basenjis are not particularly social with everyone, they're very devoted to their human. It's good that you would be able to be home much of the time. Even if they're basking in the morning sunshine from an east-facing window, a Basenji will still be keeping tabs on where you are and what you're doing. Penny will snuggle next to me on the couch for hours, loves sleeping under the covers with me at night, and will come after me with her "pokey paws" when I'm sitting in my computer chair and she wants my attention. They may be independent by nature, but that doesn't mean they're unaffectionate. Except for kisses. She curls her lip up at me when I smooch her, so I always end up kissing her teeth. Blegh.
Basenjis and how well they coexist with cats depends a lot more on the cat than it does the Basenji. Most Basenjis do well with cats if they have been raised with them. However... If the cat runs and/or is skittish, the Basenji WILL chase it. Basenjis are also quite playful. They go from sleeping to play in half a second, and they will certainly try to tempt the cat into joining in the session. A lot of cats don't appreciate this. (This is why I have two dogs, one being a mini Aussie, who is plenty athletic enough to keep up with a Basenji at play.) Our cat is 13 and has set firm boundaries with Penny. They coexist peacefully, but they're not exactly snuggling each other every day. Also, just because your Basenji gets along with your cat doesn't mean they would be kind to one that wandered into your yard. We've taken all the stray cats in our neighborhood to be spayed/neutered/rabies vaccinated, because they like to hang out in our backyard and are fair game for Penny when she gets out there. I'd hate for her to get a hold of one, but there's no stopping her when she's determined. At least they won't have rabies if she does. Haha 
One more thing to note is that Basenjis are 50/50 when it comes to be "out and about" dogs. They oftentimes have difficulty adjusting to riding in the car without wanting to be ON THE DASHBOARD (sigh), which is why Penny has to ride in a crate. She's also overwhelmed (sensory and otherwise) by places like farmers markets. She does well at dog parks, and whether that holds true across the board... well, it will depend a lot on the individual Basenji. They're all different, but most Basenjis seem to enjoy the company of other dogs.
I'll update if I think of anything more! I LOVE my little hoodlum. I could never go without a Basenji now that I know what fantastic creatures they are. For someone experienced with dogs (like yourself), they are a gem. If you need a companion for some one-on-one bonding and a deep, lasting friendship, they do that so, so well.
EDIT: And the barkless thing! The Basenji baroo is the cutest, silliest thing ever. Penny also makes a noise that we describe as "a wet sock in a trumpet." Kind of a gurgle-growl. She only does it when begging for table scraps, so I hate to admit that we've totally encouraged her bad behavior just so we can hear her talking. She can, however, SCREAM when she is unhappy. It sounds like someone is torturing a child. Before we added Daisy to the family, she would be so perturbed to be left in her crate alone that she would scream to be let out. She had a bad experience with her crate at about 9 months old (she had Giardia and we didn't know yet, so goodness knows how long the mess was there before we came home after being gone for 6 hours); she never seemed to consider it her "den" after that, even though we tried to retrain her to it using positive reinforcement. 
So proper crate training goes a long way to minimize distress, especially with a dog so strong-willed as a Basenji.
Double EDIT: Training a Basenji past basic obedience is difficult at best. It CAN be done with a lot of persistence, but my sweet darling (sarcasm, just a little) literally shut down on me in puppy class after the second session. She decided she was done laying down on the hard floor and refused any treat offered. She knows sit, down, shake, and wait. Those were accomplishments. Most of the time, her "sit" is her lowering her butt halfway to the floor and popping back up. Her "shake" is her dangling a paw in the air and waiting for me to grab it. 
