Get the things you'll need first before you start visiting shelters. There's a lot of stuff that needs to get taken care of before you can adopt - if you rent, the shelter workers will want to contact your landlord, so that they can verify that you have permissible to bring a cat home, and if you own, then you'll need proof of ownership, like a water or electric bill. It sucks to find an animal that you love and not be able to take them home because your landlord wasn't picking up their phone.
Get the paperwork sorted out first, then start looking at the animals. Tell the adoption agents what sort of personality you're looking for - they can point you to ones that they think will be a good match. Personality can change a lot between the shelter and at home, so keep that in mind. It can help a lot to keep your cart confined to one or two rooms at first, until they can adjust to life in your house.
If you have any issues once you've adopted, don't be afraid to call up the shelter and ask for advice! Most shelters will be more than willing to work with adopters to make sure that everything is going smoothly. That being said, mismatches happen. Sometimes your home turns out not to be a good fit for your cart. If you've worked with the shelter to try and solve the issues and things are still bad, then the shelter should be willing to take the cat back and try to find them a new home. Obviously this isn't ideal, but it's also better than a cat slowly driving itself into a neurotic mess because it's living in a house that's ill-suited for it. (I fostered for one of my local shelters, and it didn't happen often, but every so often I'd get a cat that just was not a good match for my household and would have to work with the shelter to find a better solution.)
Re: Questions about getting a pet
Get the paperwork sorted out first, then start looking at the animals. Tell the adoption agents what sort of personality you're looking for - they can point you to ones that they think will be a good match. Personality can change a lot between the shelter and at home, so keep that in mind. It can help a lot to keep your cart confined to one or two rooms at first, until they can adjust to life in your house.
If you have any issues once you've adopted, don't be afraid to call up the shelter and ask for advice! Most shelters will be more than willing to work with adopters to make sure that everything is going smoothly. That being said, mismatches happen. Sometimes your home turns out not to be a good fit for your cart. If you've worked with the shelter to try and solve the issues and things are still bad, then the shelter should be willing to take the cat back and try to find them a new home. Obviously this isn't ideal, but it's also better than a cat slowly driving itself into a neurotic mess because it's living in a house that's ill-suited for it. (I fostered for one of my local shelters, and it didn't happen often, but every so often I'd get a cat that just was not a good match for my household and would have to work with the shelter to find a better solution.)