Laundry room is good too if you have one.
Nope, I have a laundry “alcove” that’s barely big enough for me. 
My house is tiny and adorable, but the builders clearly didn’t have litterbox placement in mind. If this happens, it’ll have to be in the spare bedroom or the office, which is probably fine. Like someone said upthread, having a space of its own is probably a thing a cat would enjoy now and again. Especially with the dog bopping around.
My boy Theo comes into the bathroom when I’m sitting on the toilet and wants to play in my pants. But when he’s on the box in there, he gets upset and stops his business when I come in. 
OTOH, he’s right there on the sink when I finish my shower and loves to rub against my head while I’m leaning down drying off my legs. (Yes, I lean down far enough for him to do that and love him up.)
And both cats have learned through experience that I DO NOT like it when they use the box and stink up the bathroom while I’m in the shower or immediately after.
Oh yes, and get used to the idea of cat hair as a condiment. 
Regarding the litter box, if you have the space this type is designed to reduce the amount of tracking (it builds up on the ramp, but I use a hand vac to remove it). The design also keeps curious dogs out, especially if you do as I do and use a bungee cord or suchlike to hold the top on.
As for type/breed, after my previous overlady of nearly 20 years had to leave us in April of 2017 I was hesitant about another one (if for no other reason than there’s a non-zero chance of the poor thing being orphaned). But the universe had other ideas, and on New Years Day of 2018 I was adopted by a new overlady, a Japanese Bobtail. Which I wouldn’t mention but for the fact that like many of the breed, she’s actually a dog in a cat suit (that’s the consensus of pretty much everyone who’s spent time with her). Especially compared with her predecessor she’s affectionate, playful, outgoing and vocal. Especially the last. They’re not all that common, but one might be a good bridge between species.
ETA: Apologies if the pictures aren’t available — this is my first attempt at using imgur.
Cats can be just as affectionate as dogs, but most dont follow you around like dogs. However, Maine Coons sometimes do and we have two we raised from 1 day ld, and the often do.
Get one more box than you have cats, scoop twice a day. Dump the whole box and clean one every couple months, you will be fine.
Dogs clean their ass with their tongue.
Rarely are cats aggressive, dogs are more likely to be aggressive than cats. If you get a kitten, do NOT play rough with it, that will teach it properly.
Go to the pound, look at older, more sedate cats, and yes, maybe a maine coon. Get one that likes to lap sit. Maybe 4 yo? Or get a kitten.
No need to buy a pure bred, just get one from a rescue or the pound.
I’m in your position. I’ve always been a dog person. My dogs got old and died, and I’m too busy at the moment to train a new one, so we’re dogless for the time being. Our cat is great though. The litter box is no issue because he goes outside. His feet are no more dirty than anyone’s shoes.
My cat fights with me because I let him. He does claw and scratch and loves it. He knows nobody else will let him get away with that though. And speaking of murderyness, he brings in carcasses and sometimes living victims all the time. Okay, at least once a month. So we have to deal with wiping up blood and feathers and fur from time to time. Other than that, he’s remarkably gentle and kind to people the rest of the time, even strange visitors.
I do it out in the sun. Bleach is good, they also make special cat urine cleaners.
Same here, they usually stay off.
Train them not too and it* mostly* works.
They are, but they have a 2 year lifespan, while many of my cats lived to 18 or even 20. I cant take the sadness every two years.
I’m a cat guy, had cats at various times my whole life and prefer them over dogs.
I’m gonna go against the grain here and recommend a bird or something for you. Your worries are justified, and your space as described may not be suitable for a cat unless it’s an innie/outie cat, when you take into consideration things like a litter box, the aforementioned FRAPs etc. Also, cats like to be up. Thats why they get on counters, tables into cupboards on top of or just on bookshelves etc. Some of this can be alleviated by moving shelves away from windows and putting a cat tree there instead.
If only you would learn to hunt, dammit. He tries and tries to teach you, but you just don’t get it. He knows you’re not stupid, so why can’t you learn this?
That was perfect.
I don’t mind my cats getting up on things. I feed them on a small piece of counter top that turns from a odd corner. Away from the dogs. They jump up on any counter that has a sink because they like running water. They get up in the beams and on top of all the high furniture. I have 2 cat trees that they love. They hang out mostly in the laundry room, on the dryer. They have a bed there. So that is a big difference from dogs, who are normally below you on the floor. You’ll have reconcile that.
Don’t do it. Run.
Some more litterbox thoughts, since there are a variety of good solutions:
I hear you that your bathroom is too small for a litterbox, but I’m a fan of keeping the box as close as possible to the toilet, because it makes keeping it scooped so easy. When the box is far away, scooping starts to feel like a chore. My cat’s litter box is currently right next to the toilet, and it’s the work of a few seconds to flush the latest poop away.
I’ve heard the clumping litter many are recommending is great stuff. I couldn’t use it because my house has a cesspool. Instead, I use walnut shell pellets which are biodegradable. They don’t track at all. An adult cat used to other forms of litter might not like them, but my cat has never known anything else since I got her as a kitten. I’m also surrounded by gulches and it rains nearly every day - so I have taken to flinging the pellets into the gulch. I’m not worried about build-up of cat pee because of all the rain, and the waltnut shells are great compost. This would not work for everyone, of course. But it serves to illustrate that there are a variety of ways to deal with litterbox issues and there is almost certainly a type of box, type of litter, and location that will work for you.
Be cautious. Not all kitty litter is flushable; clay litter, for example, can make a nice solid clog in your pipes. Also, even flushable litters may not work well with low-flush (1.6 gallon) toilets, and can be very bad in septic systems.
If you have the cash, I recommend the Litter Robot. I only have to empty mine once a week, and it’s always freshly scooped. Hardly smells at all since the waste is sealed in the bin within a few minutes.
One cat, no problem, clean it every couple of days. Two cats, clean it every day. More than that, clean it twice a day. One box for each cat plus one extra box–although I think if you only have one cat, one box is fine.
Every cat I’ve owned has known it’s not supposed to walk on the counter. Most of them have been fine about that. But we are messy and wipe down the counters a lot in any case.
When the cats do jump up it often seems it’s because they want to get fresh water dripping right out of the sink faucet. Get your cat a cat fountain. Cats love those things. My dogs have seemed to kind of like them too.
Have owned cats all my life and this has only happened one time, with one of my cats, and it happened in special circumstances. I had a friend with really smelly feet. He had a condition. Eventually he got treatment and it went away. However, before that… He came over and took his shoes and socks off. My cat peed on his socks. It was actually an improvement. She then tried to bury them. Appropriate.
I had a roommate whose cat would pee on something of every new boyfriend she had. Like a test. Well, during the course of our cohabitation it was only two guys. Some kind of jealousy thing.
So I would say in my vast experience it is not common at all. Now if the roommate had had more boyfriends I might have a different opinion.
I had one cat claw me accidentally when he was reaching for a piece of meat I was about to give him. I was giving one piece to him and one piece to the dog and I think he was in a rush lest the dog get both pieces, not out of the realm of possibility. He ripped open my finger. Then the dog licked my blood.
I got two kittens in November, and they have scratched me a couple of times, but they are just learning. It hasn’t happened in awhile. I would say since December.
My first cat was a Maine Coon, which I had from the age of 10 to the age of 28. She was a great, great cat. But then I think I would probably have thought that about any cat I owned for nearly two-thirds of my life. I will say, she was different. She liked riding in cars as much as any dog; she liked to be vacuumed; she would help me eat food I didn’t like when I was a kid and then begged at the table for the rest of her life. She even tried to eat broccoli for me. I was grateful.
Oh, has anyone mentioned the carpet? We had this cheap carpet and two cats. They clawed it regularly, and it never showed a mark. We moved to a place, took out the carpet, and bought a nice area rug. Not cheap. These two cats ruined that rug in about a week. Got rid of the rug, kept the cats…
We also never saw a lot of wear on the upholstered furniture. Really, much less damage from the cats over the years than from puppies. Although puppies tend to inflict the damage early in their lives while with cats it could happen any time.
I don’t flush litter down the toilet, only poop.