A Bichon is a great dog for people who are used to big dogs. Because they will play catch like a big dog and behave very similar to a large dog, and most of them have a deeper bark than most toy breeds. They do not shed so you will not have hair to clean up around the house... a quick brush once a day is enough to keep the coat in check, although some people choose to keep them in a puppy cut year round which is more manageable. They are fairly easy to keep on track with weight and are a pretty healthy breed.
Pugs have a tendency to become overweight so keeping that in check at all times is important, also they have a tendency to develop Eye and Anal gland issues along with breathing difficulties all of which might require surgery. They are nice dogs but I actually consider them to be a medium sized dog not a small one, and not a lap dog.
Doxies are known to be territorial around their food, possessions and people.. Early socialization with nice children and people is VERY important with this breed. If you regularly have young children in your home I would temperament test both the parents around children as they can be nippy. They are also a breed that needs to keep their weight in check because of their length if they gain weight, it can cause them back issues the sad thing is that I see very few Doxies that are not overweight.
Of the 3 if I had a choice I would choose Bichon, based on my experiences with all 3 breeds they were the easiest for the owners to train... and they have always been the sweetest cuddliest of the 3 breeds. If you want a Lap dog with personality the Bichon is the best choice based on breed descriptions and of the 3 is the healthiest. The Bichon is on my list of dogs to own.