If you want quiet, I'd just go for a mouse or hamster. Birds are anything but quiet; mine do nothing but chatter, shriek, and chirp away all day. Finches make a constant sort of peeping and chirping noise, though it'll all depend on the type of finch. If the bird is at all healthy and content, expect it to make noise pretty well all day.
Once the lights go out, my finch and keets always stay quiet. Not so much, with the parrots; Aspen doesn't like to not be able to see me, so he lets out a loud distress call when the lights first go out. Pretty Bird is fairly quiet, but has a funny habbit of falling off her perch whilst sleeping, which wakes EVERYONE up as she screeches and clammors around the cage. She must thing something knocks her off the perch.
If an air filter bugs them, I think all of my birds would be dead (lol). I always have fans going all night long, every night, and everyone seems well rested. The 10+ hours is a must though; I often times stay up late and go to bed early, so I have to work around them by being out of my room at "bed time" and leaving the room darkened and shades drawn if I wake up early.
Cage cover? You mean to keep seed from getting everywhere, or to darken the cage? I just use a big sheet... but then again, my cages are all over 4 feet tall, 3 feet wide, and 2 feet deep, so cage covers don't really fit. I don't use them much at all though, mostly just in the summer when my room brightens up very early and they do not get enough sleep as a result.
Very important side note - whatever room you keep them in, I hope you don't like having open windows or doors
They need a high, consistent temperature. If you are one of those folks who keeps the house at about 50 and always has a window open, I'd suggest another animal. If they stay in your room, you might be able to keep your windows and door closed, and maybe invest in a heating lamp or space heater if your room is cold. My room is consistently at ~ 75 degrees to accomodate my birds. My door is seldom open, and my windows only open in the summer time. I also keep the room humid for them. So it might make your room less comfortable for you if you get a "serious" bird like a parrot.
Oh yeah, if you can get finches who are used to pellets, it can really benefit them. They do eat mostly seeds in the wild, but captive, they not only have a limited availability of seeds, but also pick and choose what they like. Mazuri and Zupreem make finch pellets formulated to meet thier nutritional needs. Throw in a treat of sprouts, some spray millet, or little bits of fruits and veggies, and you'll have a happy, healthy bird.
Finally, do see that there is a bird/exotics vet before you get your birds. Female finches love to do silly things like get eggbound, and the odd accident does happen; we had a sugar glider escapee who found his way through the WALL into my room, whereupon he ate a big chunk off of my poor little finch through the bars. The time of the accident is never a good time to be looking for a vet.
I'll post more if I think of anything.