Lateness:
My rule, allow a full hour of prep no matter what. If i want to leave the house for work at 7:00, I wake up at 6:00. Even if my lunch is packed, outfit is chosen, and I *really* could get ready in 30. I want Dinner at 6:00? I start making it at 5:00 even though it's a 30 minute meal. There are inevitable distractions and disruptions. It always takes an hour. I want to take the 3 kids to church at 9:00? We start getting dressed and ready at 8:00.
Bottom line, it's never too early to start getting ready to leave the house. And, like the oxygen mask thing, always get yourself ready first. Your kids will be cut more slack for looking disheveled upon arrival than you will.
Also:
Always keep bags packed. the baby bag stays ready to go for next time with diapers and pantry snacks stocked in it. As soon as I wash the ballet leotards/tights they go right back in the dance bag to take to out the door Tuesday mornings. Some of our random toys are stored in backpacks or bag in case we ever have to go somewhere boring that's what we grab to take. Cell and keys are stored in purse or at least next to it. It's never too early to pack a bag.
On to Clutter:
Places for everything and everything in it's place, try to get everyone in the house on *your* system.
Immediately process anything that comes in the house: mail, backpacks, lunchbags, whatever's been purchased on errands, etc.
I divide my house into 2 staging areas (in my mind)- primary and secondary. primary area is the main living area downstairs- front room, dining, kitchen. Those rooms are my focus on staying clutter free. Secondary area is the two bedrooms downstairs and the upstairs. So if I bring stuff in the house, even if it doesn't get put away, it at least goes to the secondary staging area right away. My babysitter is not really onto my system (refer to #1, ha!) so as soon as I get home from work I tidy up my primary areas immediately and get all the clutter back to the secondary areas to be dealt with later.
I also never leave a room empty-handed. If I come in from car I have an armful of trash, purse, papers, whatever with me. If I go upstairs I am taking a pair of shoes, toy, bill-to-pay with me.
This goes without saying probably but you should have lots of various receptacles for things- bins and baskets for toys, baskets for mail/papers, small bowls or whatever for keys, loose change, buttons, lego men, beads, all the weird stuff that floats around.
Don't be afraid to throw away upon immediate receipt of something, homework your kid brings home- one look and in the trash. "oh what's this catalog, maybe I want to look at it later..." NOPE, in the trash. "Whats this cheap plastic spinner toy, does it go with anything...?" NOPE trash. Trash is your friend. I have never (OK very rarely) wished I DIDN'T throw something away later.
Hope this helps!