Finches are flock birds and don't do well singly. You can GOOGLE and see pics of different finch species. What I think is pretty, you may think is ugly.
GOOGLE Gouldian finch. I think those are the most beautiful finches I've ever seen, heck the most beautiful birds I've ever seen. As for quiet, I personally think all finches are quiet. Finches are also not a bird you're ever going to hold and play with. I did hand feed 3 zebra finch babies that got thrown from their nest. They made it and were fairly tame....for finches.
I have zebra and Society Finches. 3 pair and one left over from last hatch. They really need a mate even of the same sex. Not a good hand pet bird.
I keep mine in a3.5 X3.5X6' tall cage. Lot's of feeders.waterers and More nests than pairs. They do great.
I have Blue-capped cordon bleu, green singers (just fledged two new chicks), spice, black-bellied fire, gouldian (several color mutations), strawberry, orange bishop weavers, owl & gold breasted waxbill.
The most colorful are the gouldians and they are very quiet. The weavers are amazing, but only the male and only during the mating season, otherwise they look like a sparrow. I LOVE the markings and voice on the owls. The cordon bleu are beautiful and sound a bit like a red-wing blackbird. The BEST singers are the strawberry and the green singers, they both rival any canary. Look up any of the species on youtube. You can see them moving about and hear their voices.
I have about 30, in a huge Aviary, but beware they are messy and they do chatter. When I change their water and give them dark leafy greens to eat, they are just besides themselves and they chatter and chirp and chip to each other for a long time. I have Society, Cinnamon, Goudians (may have misspelled that, don't have spellcheck on my computer for some reason) and Zebra. The Owl finch are darling, looks like little miniature owls, but VERY $$. They eat like truck drivers, and as I mentioned, are messy!!!! They LOVE water and are suppose to have bath water provided almost every day. Take it out after an hour or so, or else its just plain nasty!!!!