Yes, vinyl is very appropriate for basement use, but like all other flooring types, check to make sure you do not have a moisture problem before installing it.

Most laminate flooring is considerably more scratch resistant than hardwood flooring, but it still scratches and wears when exposed to pet nails.

No. Many people with large dogs have hardwood flooring. Your dogs will scratch the floors and it will cause more wear; however, unlike vinyl and laminate floors, hardwood can be refinished in the future. Keep in mind that even under normal circumstances, your hardwood floors will scratch. That being said, as hardwood floors age they tend to mellow.