Lure, your biggest problem finding a dog may be your cat. (Not to disparage cats, but many of them don’t take to changes in their routine. Especially after 10 years.) If your cat can adjust to a dog, there are a lot of good dogs to choose from.
The purebred/ mixed breed question comes up quickly. (Did you notice?)
With purebred dogs, you know what the parents are like and you can discuss the breed with the breeder and see what purpose your particular litter was bred for. (Not just what the breed is bred for, what your litter is bred specifically for. Working ability? Personality? Trying to “fix” a trait back into the bloodline?)
With mixed breeds you get “hybrid vigor”, and (usually) fewer genetic problems.
Either choice is as valid as the other.
If you do choose to look into the mixed breeds, humane societies and rescue groups are generally (but not always) more helpful than the “city pound”. The staff gets to spend more time with individual dogs and learn more about their personality traits. There are also some fostering groups and some veterinarians “rescue” dogs on an individual basis. (You might want to talk to your vet and see if they have any dogs “in the back”.)
As far as purebred breeds, like LifeOnWry said, labs are great dogs, but they have a long puppyhood. But there a a bunch a Lab Rescue groups, you might find an older dog that fits your lifestyle.
The setters and retrievers usually make good companions. There were developed to bond with and respond to their people. Of course there’s the usual trade off. They tend to be pretty high energy.
The Brittany is a pretty dog that’s a little smaller than a Lab. Also very smart and obedient.
A rescued Greyhound takes up surprisingly little room and it has less exercise requirements than you’d think. But again it’s a trade-off. Some Greyhounds would look at your cat as a lure, some would look at it as a companion. You’d have to talk to your rescue group about this.
If you like them, the lap-dogs (toys and some non-sporting dogs) were bred to be companion animals with lower need for activity.
This is part of the lack of “definitive answers”. There are so many variables with dogs (or the people who want them) you can’t just pin down a breed with a checklist.
If you have the time and the inclination, you might try showing up at a few dog shows. This will let you see a bunch of different breeds, be able to talk to the breeders, and help you get an idea on what you’re looking for. Just sort of “browse dogs”.
The whole “male/female, whose better?” question is tough too. Again with the variables. But a neutered male and a spayed female are pretty comparable. (Of course this is comparing the same breed to each other, preferable from the same litter.) Intact males tend to roam and might get teritorial (leading to fights). Intact females go into heat one or twice a year (usually twice, but there are a few breeds that only have one heat cycle a year) causing no end of trouble.
The most convenient tool for scooping is, like Violet said, a plastic grocery bag. Easy to carry and easy to get. To “clean up” your yard, a scooper (sorta like giant tongs) works well and you can get thses at most pet stores.
You can’t take too long looking for a dog. Take your time and look at as many as you can and spend lots of time with your prospective dog as you can. It’s worth the wait.
-Rue.