Ok, I need to play devil's advocate a little bit...
You get high points for wanting to research the type of dog to get your folks
but unless you parents are going to be ready for the commitment (time and monetary) involved in having a new puppy in the house, don't get them one! Having a new puppy is just like having a new baby - that means constant care and feeding, not to mention the issues of housebreaking, exercise, obedience training, etc. A puppy isn't something you can get, leave out some food and expect it to train itself to behave properly. Our 2 dogs are 3 years old next month and we still work obedience with them every day. They are housebroken, but every time we leave town we have to pay someone to stay at the house with them and our cats. If your parents travel a great deal, getting them a dog is a bad idea. It's not fair to your folks and it is particulary unfair to the dog.
If you want something that is small, doesn't shed a lot and is a good companion animal, I recommend something like a Bichon Frise or a poodle. Ideally you should try and rescue a dog from your local humane society or via a breed-specific rescue organization.
Some other things to consider:
Terriers are very energetic and keep a puppy mentality until they are 3-5 years old. Labs are about the same way - plus, they chew, a lot. Beagles chew and bark. Pugs are small, yes, but they have tremendous respiratory issues (read that 'high vet bills'). Dacshunds have back problems. Yorkies and Maltese don't shed, but require regular grooming. Same with Schnauzers.
Labrador and Golden retrievers are BIG and they shed and they require a lot of exercise and training. I do not consider them to be good choices for apartment living, unless you plan to have no furniture in your place. They chew and they like to dig. (our 2 are part lab, so I know from where I speak). Unless you can dedicate a couple of hours each day to exercise and training, a large breed is a an unwise choice.
Go to the American Kennel Club site (
http://www.akc.org) and read their information about selecting a puppy. It is very informative. But, most importantly, check with your parents to see if your gift would be welcome. Because if it's not going to be welcome, you will save yourself and the pup a lot of heartache by not purchasing a new friend for your parents.