if you want a dog that doesn't shed, youre limited to certain small terriers (you'll have to do a little research), miniature schnauzers are another small dog that doesn't shed, miniature poodles and some poodle mixes, bischon frise (cute, but very dumb little dogs....). most smaller dogs will tend to be yippy or hyper, so will require training as soon as possible. they may be small dogs, but they will walk all over you same as a big dog if you let them. i have miniature pinshcer, and while she sheds, its about the length of and eyelash and really not noticeable around the house (ona white t shirt, yes, couch no). rat terriers and fox terriers are nice small dogs, shed minimully. chihuahuas same. yorkshire terriers and yorkie mixes. the list goes on.
most dogs will chew on stuff as pups, but you can train them not to. a better option, find a local shelter/rescue group that actually takes the time to find out about their dogs available, and find out its behaviors.