Welcome! I can't answer your questions specific to Quakers, but I can help with the rest.
For starters, You're mom is correct, but also incorrect. Birds can be quiet. But they are also going to make noise. You can't prevent this, nor should you try! Birds are vocal creatures, they use their "voices" to call to the rest of their flock (in most cases, their owners and members of the household), for play, for being happy to be alive. They aren't going to be non-stop vocal, they are going to have down time where they're just relaxing, and not to mention sleeping (yes, birds nap).
Expenses are difficult to judge. A good cage with plenty of room depends on the type of bird you get and the type of cage and size, that they require. A cage is one of the most important things you are ever going to buy for your bird. It's their home. It's their safe haven. It's where they go to sleep at night, where many play most of the time, it's their domain. IMO, you need to get the largest cage you can afford, with the correct bar spacing for the parrot you decide to get. Not all parrots need the same bar spacing; a Green Cheek Conure isn't going to do well in a cage with bar spacing for a Macaw, for example. On top of that, when you purchase a cage (new) you usually get the food dishes designed for that cage, along with boring, dowel "perches". You can't rely on just those perches, and I find it's always handy to have extra bowels. The cost of each individual perch can vary. You can find excellent deals online (we highly recommend mysafebirdstore.com ) but depending on the size, type, etc of the perch, they start at around $10 each. A good quality cage, brand new, is going to cost a few hundred dollars. Sometimes you can find a used cage on Craigslist (I personally don't recommend that, but to each their own), but you might not get the dishes, you might not get seed guards if you wanted them, etc. A good estimate is between $400-$800 just for cage, dishes, perches and toys to start with, if you're talking anything more than a Budgie or Cockatiel, and even they can be prices if you're starting off fresh. Not to mention you're going to want to get a perch for outside the cage, either a Manzanita or a portable (many like PVC) because your bird is going to need outside cage time. You need to spend time with your parrot, handling them and playing with them. How much out-of-cage time are you anticipating giving them?
As far as monthly costs, that also varies. Some birds go through toys like they're water. Some may play with their toys but aren't necessarily destructive with them. I've had the same toys for my GCC since I got him in October, with the exception of 2. I also rotate them out, I purchased enough that when I do the weekly cage cleaning (you need to change papers every day, but should do a good scrubbing of the cage once a week, which I'll get to in a minute), I can rotate new toys in and give the other toys a break, except for a few that he's attached to, like his bell. Toys aren't cheap, unless you decide to buy the cheap toys you see in the grocery store and for most parrots, I wouldn't recommend a large majority of those anyway! Good toys can cost $5, and I've seen some that are a significant amount more. I highly recommend a large variety of toys, from foot toys to preening toys, because a bored parrot is a bad thing. You can also opt to make some of your own toys, and there's plenty of how-to's in the DIY section of the forum. There's some fantastic ideas in there! But the supplies aren't necessarily going to be cheap either. It can be more cost effective, if you have the time and inclination.
Food also varies. On top of pellets, or a pellet seed mix (personally I give seeds only as a treat for the oils, it is not my birds diet staple ever), you need to give them fresh fruit and/or veggies
daily. Pellets can vary in price, depending on where you get them, how much you get and the type you get. I feed Zupreem Naturals and I can get my food for $2.99/lbs by buying it at a local store where I can purchase it by the pound. A bag retail of the same exact food, costs $14-$18. Depending upon how much your bird goes through, that could last you two weeks, or it could last you 2 months. The larger the bird, the larger the feedings, the more food you go through.
Vet bills are also a variable. Whenever you bring a new bird home, you should take them to an Avian vet as quickly a possible - some even say before the bird enters your home. A good Avian vet can cost a pretty penny, but in most cases, you may only have to visit the Avian Vet once a year, for a general check-up and cultures and bloodwork to ensure the health of the bird. The problem with birds is that they usually don't show that they're ill until they are at deaths door. You could also end up having your bird get injured, and then off to the Avian vet you go, unexpectedly. Your bird could get ill and then you have to go to the vet periodically. So, obviously, it all depends on each individual bird and situation.
You can learn to clip your birds wings and toenails yourself, but I highly recommend finding a local bird store/shop and seeing if they do complimentary clippings. I get my birds wings and nails done for free. The rate of how often you need to clip, depends on how fast your birds wings and nails grow back. I recommend someone else doing clippings as it keeps them from associating you with the restraining

Some may also tell you to leave a birds wings full flighted. Personally? I've seen way too many birds get lost that way, I've seen way too many birds come in to rescues after being lost, because they were able to fly away.
As far as mess goes? Birds are messy. You are going to have to do some cleaning every day. If you have carpet where you keep your bird, vacuuming every day. Changing their cage liners every day (or you can use a type of bird "litter" which allows you to scoop out the poop, much like kitty litter and then do a complete change out once a week or every other week). If you have hardwood, sweeping every day. I also recommend that once a week, you remove everything from the cage and give it a good cleaning. I do this simply by using an old washcloth and wiping down with a vinegar solution. This is also when I take both the grating and the catch pan and scrub them out with water and some soap (I use dawn, which is what my Avian vet recommended). I also do the wooden perches with just a wet rag, unless they're rope. Once everything is dry, back in they go.
So there's my $5 for ya. I bet you didn't read it 'cuz it was so long
