I have a bichon, and your description really did make me think of either a maltese or bichon. The two are closely related: the "dog part" is very similar, but maltese have straight hair and bichons curly hair, and bichons are larger. Maltese are a toy breed and are usually under 10 lbs, while most bichons are more in the 15 lb range, though of course individuals of both breeds can be larger than average.
Comparing the two breeds, I would say that of the ones I've met, both are usually friendly with people, but some maltese seem to be "yappier" and less dog-friendly than bichons. This may be because they're so small that the owners are nervous about socializing them with other dogs. If you want to put your dog in a tote bag and carry it everywhere, a maltese is more the right size for that. On the other hand, maltese can be very tiny and fragile; a bichon is probably a better bet with children for that reason. Of course, it depends on the age of the children and how gentle they are. In general, I'm not sure I would recommend small dogs for most young children under 8 or so. A bichon might be ok with gentle children from 5 to 8 and would probably be ok with most kids 8 and up, but for a maltese the kids should be older (maybe gentle 10 year olds and up). This is just my opinion, naturally! My bichon is good with kids, but is usually around them in small doses and I always keep a close eye on the proceedings!
Bichons are allegedly hard to housebreak, though I didn't really have any problems with mine. I don't know about maltese in this regard. Other than this, both breeds should be easy to train -- they are very smart and eager to please.
My bichon has a "bad home haircut" -- basically sort of a medium length all over. The bichon fashion police would probably accuse me of neglect, but I think he looks perfectly cute and more normal than the poofy show 'do.
Probably more than you wanted to know about bichons and maltese, but you might want to check out the web page for Small Paws Bichon Rescue at
www.smallpawsrescue.org.
Good luck with your search!
Audrey