If your parents insist on that breed, advise them to adopt a purebred from a rescue.
Even though your friends own a pet shop, please dont get your puppy there, you will be supporting puppy mills, and that is something that has to stop.
although im sure the poor little guy needs a good home, and to get out of a *$&%(# cage.

obviously both breeds have long hair that MUST be cared for,
maltese, have a very cotteny texture to their coat that causes a lot of matting, shih tzus are a bit easier,

they can both be temperamental and barky like any breed, i would be much more concerned about health issues. if they get the puppy, get it to a vet immediately.