Hello and welcome to the forum!
I am currently owned by 4 cockatiels and I've been owned by a total of 5 of them in my life....plus, 2 budgies/parakeets.
I absolutely LOVE my tiels! My male tiels both talk and my youngest, Chicken Little, talks quite well for only being approximately 1 year old this month. (You can see a video of him talking by clicking the link in my signature line.)
Our tiels love to hang out with us while we're on the computer, reading a book, cooking dinner, watching a movie or having an afternoon snooze. Chicken and Chiquita will sit on my shoulder and snuggle up to my neck, preen my hair, preen them selves, take a nap. (They aren't as active as our Conure is, he thinks we are his human jungle gym...that can get exhausting.)
Our tiels love to share our dinner and each has a rather unique personality. Chiquita we call "Messy Beak" because when she eats something she really loves...like butternut squash or sweet potatoes...she gets globs of it all over her beak and just keeps eating. Unlike Sweetpea, who takes a bite, cleans her beak, takes another bite, cleans her beak....
Chiquita absolutely LOVES my spouse and I always envision her having long black eyelashes, like Tweety Bird that she'll flutter at my spouse everytime she see's him. (She's a beautiful Lutino Tiel)
Chicken Little is very studious...he's a very fast learner and loves listen to me talk, he'll put his face right up to my lips and watch and listen, and within a few weeks...he's saying what ever phrase I wanted him to learn.
Charlie and Sweetpea are rescue tiels who were horribly neglected and probably abused at some point. I've had them since August and both have come a very long way. Charlie didn't know any verbage at all...now he talks almost as good as Chicken and he's not screaming everytime we walk by his cage. He loves to come out and walk with his wings out...we call him "Tough Bird"
The last few weeks he's made tons of progress with hand taming and actually seeks our attention and companionship.
Sweetpea, has quit hissing everytime we get near and is coming out of her cage on her own and when she's ready to be put away, she'll get on our hand without fuss and she's sooo flippin' sweet!
If you are looking for specific qualities in a bird, my best advice is to look into one that is hand tame, no matter what the breed. So if you want a cuddly bird wait to find one that's been handled and is a "proven" cuddler.
As far as the budgies go...they were my first birds. They were awful cute, but I didn't know much about birds and we didn't have the information highway of the internet at my fingertips. I never did get them hand tame very good, they were more interested in each other than human companionship.
I think, if I had them now...our relationship would be wayyyyy different as I have so much more knowledge and experience now.
I hope this helps a little bit.
Good Luck!
Toni