It really depends on the individual dog. My first dog as a teenager was a Dalmatian lab mix who was fine with my cats, parakeets, goldfish tank and rabbits outside. Had other issues but we knew nothing about raising and socializing dogs so he wasn't socialized right and developed fear aggression with people. Very protective as a guard dog but I had to confine him as he'd bite any stranger so too protective to be safe in public or even loose with company. Bit a few extended family members.
My Akita pitbull mix was amazing fine with cats, very protective had resource guarding with other dogs so not a dog park type. I took him once and he ignored all the other dogs and stayed hyperfocused on fetch with me. Took a lot of training to keep him not aggressive with strangers and other big dogs. Lots. I did it all myself but it was a lot of work and a lifelong management. He was perfect for me and had perfect recall and got to love strangers but had a sixth sense about people. Had individual dog friends but I always had to keep all food, water bowls, treats, toys away or he'd attack. I could never pet the other dogs or he'd get jealous. Very strong on the leash but he was so good loose I never bothered to leash train him much and let him loose everywhere. Fine alone all day I kept him in his own room to be cautious about cats. First dog fine alone all day too.
Current dog mix of all kinds of things according to DNA testing. Boxer, lab, Chow Chow, pitbull, German Shepherd/shepherd/herding/hound, labs and gsds are most likely to get separation anxiety and be was given up by first two homes so he has bad separation anxiety. Now I can leave him alone 8-9 hours a day maybe every other day and alternate with doggy daycare. Every day I think would be too much for him. Maybe he'd be ok with a dog walker if it was the same one but he's very protective and barks and growls ferociously at any sound or any intruder at car or apartment. He's never bit anyone but if I'm not home to say it's a friend I don't know what he'd do. I wouldn't want anyone to get bitten. He never makes a sound when I get home so he must know my walk. I read dogs can tell their owner's individual car engines sounds. If it was the same dog walker he'd get to know them but the companies here all rotate and are more expensive than the doggy daycare that he loves. He's fine with my cats they're all buddies. I don't have a good room to lock him in separately so there's a baby gate that they can escape to that he can't get into. He needs medication for separation anxiety, not all dogs do. He loves other dogs and took a lot of training but now loves new people and is very friendly. He's a little of fun to take to the dog park and out in public and know he'll be well behaved so that's relaxing to be able to trust him in that way and not have to worry he'll fight with another passing dog. He seems to know when we're out in public it's social party time and he has to be friendly and polite. Vs at home or in the car or walking me alone at night he has to protect me and is very alert and not friendly. Same as my last dog. I couldn't relax as much with other dogs and my last dog but he would ignore them after much training. On the other hand he was perfect loose and would never leave my side or run off and always come back instantly the second I called no matter where we were. This dog won't which is very stressful when your dog runs off and won't come back or escapes and you worry about something bad happening to it. Also my last dog was much cheaper, had no health issues til an injury and surgery at age 7, could eat anything and everything no stomach issues, could stay alone eight to ten hours or longer no dog walkers or money and no accidents and I just had to play fetch or let him run anywhere a couple of hours after work. Easier and cheaper. No inflammatory bowel disease, no food allergies or expensive diet, no stomach meds and vet visits, no separation anxiety, no behaviorists or medications. This young dog is a lot more expensive.
Whatever you get, get pet insurance right away. It's cheaper the younger and healthier they are and the rates shouldn't go up with age or new medical conditions. Unknown mixed breeds are always cheaper than any identified breeds so better to stay ambiguous with insurance. Unless you have DNA testing you never know anyone, visual guesses aren't very accurate anyway.
So all my various mutts were very good and bonded with my cats. I've had from two to seven cats at a time. It really depends on the individual and you have to be very firm and consistent from day one. Never tolerate one second of any resource guarding or rough play from the dog on the cat since the dog is so much bigger and can accidentally hurt the cat. Let the car be assertive and be boss over the dog but not provide or torture the dog either.
Most dogs have some instinct to protect their homes and families. Many dogs can learn to be home alone for eight or more hours it's easier for adult dogs than puppies or adolescents. The dog breeds and mixes who are bred to bond the most with their people like German Shepherds, labs and I think boxers get the most clingy and most likely to get separation anxiety.