Are you sure you want a parrot? In my experience, other animals are more gentle, cuddly, reliable and predictable in their behaviour. A parrot is basically like having a noisy, messy toddler around who can also fly and has pliers/a canopener attached to their face (depending on the size of the bird). It's a huge commitment.
Parrots often have a very strong sense of what they'd like to do, and this isn't always aligned with what their humans would like them to do. You can't predict whether a bird will be gentle, especially as parrots can change when they reach puberty and adult hormones (and the desire to breed) kick in. Touching a parrot anywhere apart from its head and neck isn't advised as only bonded pairs do that - stroking its back, belly, vent, wings and under the wings gives the parrot the message that you're its mate, which can lead to aggression towards others in the house as it tries to drive them away from its chosen partner. Most birds don't like to be cuddled and held close - I think it reminds them too much of being caught in a predator's grip.
Parrots have subtle body language and if you don't pay attention to all the signs they're giving, they can and will bite. Parrot beaks are designed to crack open seeds and nuts and to chew up wood - their bites draw blood. At some point, they will destroy at least a few of your possessions if they have access to them - furniture, books, toys etc - unless you are very careful.
Most parrots live a long time - many will live for decades and could still be around when your children have left home. They need at least 2-3 hours out of their cage a day; unless you have a completely bird-safe room, you have to supervise them. They can also be sensitive to their environment and can be distressed by changes (new people, different routines and so on) which can lead to behavioural issues like plucking their feathers.
Even the gentlest, most affectionate parrot is going to have days when it wants to do its own thing, or is more interested in destroying a toy than playing with you, or doesn't want to be touched. I think Leia is wonderful and I love her very much. However, sometimes she doesn't want her head scratched and will tell me so, it's taken her months to not go into a (pretty mild by parrot standards) strop at the sight of my sister, she doesn't say any human words but I'm becoming more accomplished in Pionus, and while she's a species known for being quiet, she still has a loud squawk that she likes to deploy when I'm on the phone. Our relationship is more akin to companions than owner and pet - she has a lot of autonomy and chooses to spend time with and on me, but it's her decision and I don't force her into it.
I think what you're after is a really well trained, calm dog or a cuddly, sociable small pet like rats (as long as you can handle the short lifespan - they only live for two to two and a half years). I've had both for years and they're both much more tolerant of human handling, love interaction and cuddles, show affection in ways that humans can easily interpret, want to be around people, and are playful and intelligent. Rats need to be kept in pairs/trios at least and they'll need a large cage, a varied diet and suitable enrichment, but are much quieter than birds. I trained mine to come when they were called, and they loved snoozing inside my jumper while I worked at home.
This isn't meant to sound like a rant or me telling you off or anything - just that going by your list of things you want in a pet, parrots don't sound like a good match.