To clear up some confusion with regard to the cockatiel....they are not large birds, but they are larger than a parakeet/budgie.
YES! Cockatiels CAN learn to talk and quite well and also learn a whole lot of tricks. I've been owned by 3 male cockatiels and all 3 of them learned to talk, in my signature line is a video clip of our youngest male tiel...Chicken Little chattering up a storm.
If you have a moment..check it out!
Cockatiels have fabulous personalities and can be very wonderful with children. My suggestion...if you choose a cockatiel is to get a hand tame tiel that you can handle up front. If you don't have any bird experience, it can be very frustrating learning to hand tame any bird species.
Our first cockatiel we got when my children were quite young, 5, 6 and 10 and they learned how to safely handle Chaco Bird with no problem.
The biggest downfall to the cockatiel is that you mentioned allergies??? Tiel's are a powder down bird and they have a lot of extremely fine dust that can really aggrivate allergies. However not everyone with allergies is allergic to cockatiels. And regular bathing along with an air filter/purifier really helps in keeping the dust down.
Cockatiel Hens are very much quieter than the males, they chirp, but the males have a greater tendency to talk and whistle. I found both male and female tiels to be very easy to handle and I've not found one sex to be more nippy or bitey than the other. For all our tiels, once they're hand tame, we've not been bitten at all.
My experience with Cockatiels is that they don't have the unpredictable independent behavior that sometimes comes with other parrots, such as conures. Our conure is very much a lover and a bully. And he will sometimes haul off and bite for no particular reason or sometimes he get's over excited when playing and becomes rather nippy. That mouthy/nippiness can be frustrating if you aren't experienced. Also, my experience with our conure is that he is an "exploratory nipper" meaning that he's constantly mouthing, tasting, test biting as his way of checking things out. We've been consistent with our expectations of what's allowed and he's learning all the time what the "testing" limit is and is MUCH nicer to handle then when we first got him.
I think that cockatiels make a wonderful first bird, their only downfall is they're powder down. Aside from that I wouldn't hesitate to recommend the cockatiel to you as a first family bird. If you want a rather quiet bird and don't care if it ever learns to talk, then look for a Hen, if you'd rather listen to chatter, whistling and hope it learns to talk, then look for a male.
Good Luck and happy searching!
Toni