Well I have to be honest - the budgies I've kept in the past sqwaked more than what you would might call "song" - in fact they came no where close . They were non stop manic screechers and made an allmightly mess so I have to say that are not my most favourite "pet" bird.
Well i have one budgie at the moment (i used to have four -but my ex has the other 3) I have to admit that the whole reason i have a budgie is for the cute noises they make. My budgie wakes me every morning with his chittering and the odd tweet and its lovely. Admittedly he has squaking tantrums which don't sound pleasant but he only does that when he wants something. I've had budgies throughout my life they are great birds with great personalities. I had a cockateil at one point and even though it didn't make as much niose as the budgies but when it did make noise it was Super Loud!!
If you want a budgie try and get a young one , preferably direct from a breeder if possible. that way you can get it used to being handled and it may even learn to talk. Good luck
None of the parrot species are particularly "singing" birds, well except for the ones who learn to sing like a human! I'd agree that budgies chatter more, but tiels are louder when they call out. I actually think tiels tend to have a more musical voice when they are just happily chirping. In my experience, the more attention and time you give either one, the less likely they will be to screech a lot. When I had a male tiel, he really only screeched if he wanted something, i.e. his food dish was empty or I left his cover on too long in the morning . If you get a baby keet, the best thing you can do is handle him/her lots and talk to him/her a lot. I'd agree to avoid putting mirrors in the cage. Peepers chattered a lot but he talked so well that a lot of his chattering was actual talking and a pleasure to listen to
I suppose mine were perhaps overly noisy as I took them from someone who could no longer keep them. They were never particulary well handled (where they came from) and certainly not youngsters either, so really wanted next to nothing to do with us. They squawked even louder as we approached the cage and would always flap around frantically if we tried to feed or change water
So I suppose the way to go would be to get a young chick and handle it la ot....
. They were non stop manic screechers and made an allmightly mess 
so I have to say that are not my most favourite "pet" bird.
Well i have one budgie at the moment (i used to have four -but my ex has the other 3) I have to admit that the whole reason i have a budgie is for the cute noises they make. My budgie wakes me every morning with his chittering and the odd tweet and its lovely. Admittedly he has squaking tantrums which don't sound pleasant but he only does that when he wants something. I've had budgies throughout my life they are great birds with great personalities. I had a cockateil at one point and even though it didn't make as much niose as the budgies but when it did make noise it was Super Loud!! 
I'd agree that budgies chatter more, but tiels are louder when they call out. I actually think tiels tend to have a more musical voice when they are just happily chirping. In my experience, the more attention and time you give either one, the less likely they will be to screech a lot. When I had a male tiel, he really only screeched if he wanted something, i.e. his food dish was empty or I left his cover on too long in the morning 
