Help me choose a bread please

[Nochangeplease]

I’m hoping to be able to get a dog next year. Something I’ve wanted since I was a child. I know it’s hard work and I want one so badly that I’ll overlook the mess, the sleepless nights ect.
So there’s me and 2 kids both over 8. I work in a school so I’m out from 8-3:30. Can pay someone to come over during the day and would originally get plan to get a puppy during my 6 weeks off.
I’ve narrowed down several breeds but would love some opinions based on my preferences.

1. Good with kids
2. Easily trained
3. Not big
4. Doesn’t bark a lot
5. Doesn’t need loads of exercise because I can’t do this every day. But capable of coming on long walks on days off.
6. Doesn’t suffer terribly with separation anxiety.

I should also mention I do not have a garden. Willing to walk before and after work though but realistically these won’t always be able to be long walks.

@wwud12 yes we have a lhasa too , she's needy, would prefer to be permanently touching you but puts up with being in the same room when you refuse to let her stay on your lap. She barks at a sparrow's fart or at anything that moves or she suspects might move at some point in the next five hundred years (or so it seems) She is lovely but she would be a nightmare to have in a flat.

I only know two miniature schnauzers but both of their howls/barking go right through me - terrible noise.

@Gifgif I know 3 - all school run dogs and all incredibly noisy at the school/park gates

@midnightstar66 it's horrible isn't it? The canine equivalent of chalk on a board.