S.B.
I have had cockatiels. I got my first when I was 15. And they make great pets. They can talk a bit...although it's often like a toddler... only the family can recognize what they are saying. They also whistle tunes, mine loves to sing Reveille. I am not sure how they compare to lovebirds. They are a commitment, they live 12-15 years, but my cockatiel that just passed away this weekend was 23 years old.
They aren't as destructive as some of the larger birds. About the worst mine have ever done is chewed the edge of the ceiling fan while they were getting some free time, but even then I think I was the only one who noticed it. Watching them closely and giving lots of attention, can help keep them from being destructive.
MOST of the time they are relatively quiet. But they do have periods where they can get a bit noisy. Usually I just close the door to the room they are in, but if they are really worked up, covering the cage usually does the trick and quiets them down. In the past I had a breeding pair, and they would get a little rowdy during breeding season.
There is no need to buy a pair, like someone mentioned earlier..two birds bond to each other. A single bird is more likely to bond with the family.
Most birds that are hand fed and raised don't bite unless they really feel threatened. Make sure you get a hand fed and hand raised bird!! And you will have to teach your children how to properly handle the bird. I have a three year old and he handles my birds with no problems, but it did take time and patience to teach him. And I still have to watch him closely, I won't leave him alone with the birds while they are out and about. And I keep an eye on him when he gets near the cage, sometimes he wants to share his lunch with the birdies.
As far as the mess goes...I have been feeding mine pellet food for years. It's nutritionally better for them. I had a female bird years ago that wound up with a vitamin deficiency because I only fed her seed, the vet recommended pellet food. Millet and seeds are a treat for my birds, not a staple. Pellet food is less messy because they aren't shelling any seeds. . It does get thrown or tossed a bit while they eat it. I have had success in taming the mess with a mesh cage guard. I tried a few other guards, including expensive fancy ones, and the cheapy mesh seemed to work best. I also have food dishes that have longer arms, so they set back in the cage a bit. I layer newspaper, using several sheets, so I can just lift the top layer on a regular basis. About once every two weeks or so I really wipe down the tray. And about once a month I try to scrub down the whole cage.
Frequent baths will keep the dander down and keep the birds clean. And most birds love it! I just fill a spray bottle with warm water and spray my birds down. They love it! But there are people who put their birds in the shower or sink - perches are sold just for this purpose.
I know this is long, but I hope it helps. Good luck with your decision!