in terms of everything your looking for.
chihuhaua: can be yappy and hard to housebreak, if adopting an adult look for existing behavioural problems, this is a GREAT breed for the right home, but bad breeding and too much papmerping an dlack of disaplin as puppies can destroy a chihuahua (all those bad chi stories you hear)
the chihuahua is relitivly high energy for its size and while it can get enough excersize playing a good game of chase aorund your livingroom, they will need a daily walk, some outside playtime and lots of socilization...purse living and chihuahuas can be tough as many get down right visiously over protective of their carriers (and their people!)
(i have always had chis and love them, but they require a firm yet kind hand, alot of structure in their lives, plenty of excersize relitive to their size and LOTS of socilization)
i woudlnt suggest a pap. pappillions are a high energy breed who likes to run and play, they make WONDERFULL agility dogs, but i have high doubts one would make a very good choice for a purse pup.
mini doxies...possibly the perfect dog for you...
some can be barky, but compared to chis there relitivly quiet. there a mid energy breed (stanrads are definatly a higer energy level than minis) and like the chi would be content with a good run around the apartment but should get at least 1 daily walk too.
my biggest concern with doxies and purses is the back issues they can get. youd need to be very carefull with stairs and jumping off furniture too. otherwise great little dogs.the grooming of the shorthairde is relitivly simply but the nails are fast growing!
other breeds to look into. chinese crested, the hairless and hairy hairless have moderate grooming needs due to skin, powderpuffs need a daily brushing and a weekly bath but no skin issues like the cresti, at 10-13 lbs there on the larger side of the "purse pup" range but doable (and ive seen some absolutly adorable 5-7 lb chihuahua x chinese cresteds in rescue that are just too cute!)
i would not suggest terriers, yorkies and silkies as cute as they are are true terriers and have the enery of one.
a small maltese kept in a puppy cut might work, same for a bichon, toy poodle would be good size and personalit wise but lots of rooming upkeep on that one.
an adult would be perfect! good for you for looking into rescue!
as a side note, ANY dog can be "yappy" and ALL dogs can be taught to be quiet on command. training! thats all it takes, both my chis know when i say quiet its time to hush, and they do!