Well you get puppies from rescues as well, just to make it more complicated, lol.
Puppies are definitely hard work, it is a bit like having a baby - but on the plus side you do get a blank slate and they are easier than kittens in that they actually do want to learn to please you, rofl.
You do get completely perfect rescue dogs looking for a home and you get ones with horrendous issues and lots with fairly minor stuff where they just need a bit of training or just that they do things that they're used to being allowed to do but you don't want them to.
A rescue should definitely be able to find you a dog that suits your household, with young children and a cat it might take a bit longer to find the right one, but obviously getting a dog isn't something you rush into anyway.
Training a dog is pretty much like looking after a toddler tbh, lots of praise and rewards when they do something you want, distraction when they do something you don't want them to but that isn't a big deal and a firm no when they do something you really don't want them to. If you've never had a dog before I'd go to classes and they should help you get to grips with teaching commands.
Dogs are harder work than cats, by a long shot - you don't ever get to a point where your dog is 'done', if you stop reinforcing commands - they stop responding to them so training is an ongoing thing. (though obviously not as intensive as in the beginning) and having to go for a walk whether you want to or not can sometimes be a bind.
They're great though, they're pets, best friends and entertainment all rolled into a waggy package.