All birds are going to be a little loud... but there are some that`re appropriate for apartments and the like. The most important thing it so meet all the types of birds you`re interested in, bring anyone you live with, and listen to them. Make sure that everyone can tolerate the sorts of noises the birds make.
Personally, I don`t think there`s such thing as a `starter` or `beginner` bird. Read as much as you can, find the bird you`re interested in... and get it. As long as you`ve done your homework and made an educated decision, that`s all that`s important.
Typically budgies (parakeets), cockatiels and lovebirds are the three birds most considered to be `starter` birds. They each have very different personalities and vocalizations. Budgies are very playful, but in my experience not very cuddly. They`re the most high-energe of the three.
Cockatiels are much more laid back then budgies. They tend to be much more cuddly, and a considerably less playful. They still play, but they don`t have the boundless energy of a budgie.
Lovebirds are SASSY. They tend to have very bossy, dominant personalities. They`re quite opinionated little birds and are afraid of nothing. I think they`re hilarious.
Other birds you might consider:
Parrotlets are small, quiet and playful. They`re often described as big personalities in little bodies. Like lovebirds, they`re FEARLESS. They have a reputation for cage territoriality, so that`s something you may have to deal with at some point.
I also love the pyrhurra conure family. These are the `quiet` conures. They include green cheeked, maroon bellied, white eared, painted, black capped... Black capped conures are my personal favorite. These small little conures have very soft voices in my opinion. They`re playful, mischievous, wonderful little birds. They like to play on their backs, so they learn easily to lay on their backs in your hand and play or cuddle that way. You`ll also occassionally find them sleeping on their backs on the bottom of their cage. It`s given a good number of owners small heartattacks as they think their poor little birdie is dead! It`s led to more then one bird getting a very rude awakening.
I`ve heard that pionus can also be quiet, but I know very little about this type of parrot.
I encourage people to get their birds from either a quality breeder (the type that will make sure you have a good education on bird care and as you lots of questions to make sure you`ll take good care of their baby. When you find that kinda breeder you know your bird has gotten the best start in life possible)
or from a quality bird rescue. Most bird rescues will require you to go to at least one bird-care class, so you`ll learn the most up-to-date info on parrot care. Since the goal of a good rescue is to find a good PERMANENT home for their birds they won`t misrepresent their birds to you, or mislead you. If the bird has any health of behavior problems they`ll let you know that immediately. Rescues can often get in birds that`ll make perfect pets, with no major behavior problems, simply because some sort of upheaval in the owner`s life forced them to rehome their birds, or because the owner couldn`t afford some sort of important treatment for the bird (like setting a broken limb). A good rescue will make sure the bird is completely recovered before putting it up for adoption. So please don`t count out a rescue. I know some people think all the birds from rescues come with heavy baggage and issues you don`t want to deal with, but this isn`t always the case. Let them know this`ll be your first parrot, and they`ll try to match you up with an appropriate bird. They don`t want to overwhelm you, since their goal is permanent placement.
I personally find working with the rescues to be more rewarding, but it can be a royal pain in the rump. I hope some of this helped. Just try to decide what kind of personality of parrot appeals to you, pick a few species to research in depth, and then go out and meet those birds. Interact with them, and listen to them. You`ll find the right bird!