@blessed4 I would suggest a Bichon Frise the most because the other 3 don't quite match.
Both the Pug and Shih Tzu are prone to health problems because of their flat faces. As you mentioned, when they have to go to a vet for these problems, it will most likely not be covered by insurance. Also, why would you want a dog that is unable to breathe normally? But that's just my personal opinion.
Regarding the Dachshund, they are not really suitable for first-time dog owners. They are very vocal and extremely stubborn. If you really want a Dachshund, talk to some owners and breeders about what they are like. I absolutely love Dachshunds and their crazy personalities, but they are not easy to handle.
The Bichon Frise (or their smaller cousin, the Maltese) is more easygoing, happy, and playful. With good socialization, they are usually very friendly to people and less likely to bark. I would also suggest looking at Toy Poodles. They match your requirements but have a different personality than the Bichon Frise.
And one last thing, please keep in mind that small dogs can easily live for 15 years or more. Your (and your sisters) life will probably change a lot in the upcoming 15 years, will a dog still fit into your life after 5, 10, or 15 years?