@Whoalookitsme:
The Cat: I adopted her when i moved into my apartment she is now almost two years old. She is around dogs at my apartment and at my parents house. Each dog she is different with. The Great Dane at our apartment.
hi Whoalookitsme, glad you found the forum. It's great for everything basenji! And congrats for doing homework on finding a breeder you like. Also love your name - sounds like a good horse to bet on at the track!
I am just waiting to be a basenji owner and my comments are going to be my opinion only. So please don't take offense. You and others on here might not agree with them. But what I like about this forum is that you can share knowledge, experiences and a host of other things with those who love the breed.
Here is a few things you might want to really think about:
SPACE: My husband and I live in a large 3 bedroom rancher with a backyard, though the backyard isn't acreage or anything like that. Do you know what my concern was? Would my pup have enough room. A breeder even mentioned this to me - about our backyard not being huge. I know that there are people successfully living with basenjis in apartments, in fact someone on this forum has posted pictures of their dog in their apartment, but if I lived in an apartment, I don't think I would choose a basenji. Cats? You bet. Really small dogs - maybe. But not a basenji or a great dane. I can appreciate how much room your great dane already takes. 
Also, regarding your apartment, don't just think your basenji will just chew furniture. Those nice wood door frames are awfully tasty too. So are the cupboard doors.
YOUR SCHEDULE: A puppy is really going to need more than exercise at the dog park a couple of times a week. I think it will need at least a couple of really good walks every DAY. Exercise (all out type) is just so vital for their health. You mention you are a junior. I've never seen what the schedule is like for someone training to be a vet, but isn't there more demand on your time the further you get into your program? Just a question. Regarding showing, I am in awe if you could fit that in with all of your studying. I would think all of that would be a big load for someone working so hard on a degree.
THE CLASS: Horses are prey animals - that might be tempting for your basenji unless he is really well mannered. I would like to offer a caution (and I used to ride TONS and are familiar with horses) - a green colt is really going to put out that kind of nervous energy a dog can pick up on. Again, just my opinion, but it might not be the best of pairings. So if you don't bring your puppy with you, will he just be at home alone with the dog and cat? I remember being a student, and I would not have been able to afford doggie day care. 
TRAVELLING: Well, we have a very wonderful member on this forum who does a LOT of driving, and the basenji goes along. AJs Human drives a semi, and AJ goes along. Again, in my opinion, that takes a special kind of dog and owner combination, bond, love and understanding. The hour long drives in a vehicle won't be the happiest times your basenji or cat will have (my cats hate the 7 minute drive to the vet). But oh how a puppy would like that hour to do some good hard playing or training with you. I'm not saying it can't be done, because basenjis that compete in shows do HUGE amounts of travelling, but I think that travel time is often offset with lots of playing and just being a basenji.
Never apologize for a long thread. You are obviously thinking this out carefully, and you are to be commended for that.
Remember, I am giving you only one opinion. With whatever information you get, absorb it and toss it around in your head for a bit. Then, in the end, you will know you spent a lot of time and consideration making your decision.
All the best to you.
