When cleaning up after dinner, prep things for following evening's dinner - peel potatoes and soak in water, peel veg and soak/pop in airtight box, defrost meat or a previously cooked sauce, marinade meat, maybe even make the sauce.
By sauce, I mean a spag Bol, chilli, curry, tagine, stew etc. So you just need to reheat that when you get in and cook the rice/pasta/couscous/potato etc.
I like to make a double batch of the sauce part and freeze the 2nd half for another night in the next couple of weeks.
Also, if your oven or a slow cooker can be set up on a timer, that could be really useful for stews etc or for 1 tray roasts or having baked potatoes and a small joint cooked when you get in to just steam some veg etc.
We work on laundry by keeping on top of washing and drying dirty things but putting all clean dry clothes into a clean laundry hamper to fold at the weekend while watching tv. Anyone can root about in the clean hamper if they need something but it feels less of a chore doing it this way. (And DH does the ironing in front of countryfile on sundays).
Get a bunch of cards for birthdays, anniversaries, and others you would generally send (condolences, accept/reject invites, good luck/well done, get well soon etc) so you can grab one to send out quickly. And get a good few stamps to be able to send at short notice without needing to go to PO.
The 2nd stage of that is to have wrapping paper, tape, ribbons, (and boxes/tissue paper or bubble wrap etc if you need to send by post) all ready to be able to wrap presents easily. I had a generic presents drawer when dd was smaller and had parties to go to but not anymore now she's a teen - but I tend to try and get presents well ahead of time or pick up things I see that I know particular people would like later.
Automate bills etc where possible - direct debits where you can or get bank details to be able to use banking online at a time that suits you.
Yes to regular food shopping slots and cleaner.
Not for everyday use but shortcuts at pressurised times include the sachets of instant rice or noodles for stir fries, frozen uncooked prawns (defrost and cook very quickly), tins of tuna/sweet corn/bamboo shoots/4 bean mix/coconut milk etc.
Do a big check of cupboards and a large stores shop before you start - for food, cleaning items, drinks, treats, medicines, first aid items etc - all the things your family goes through relatively frequently (like we use a lot of heat and cold patches for muscle injuries but almost no indigestion remedies- so think about YOUR families' needs).
And keep a list on the fridge door which you ask everyone to use: anything they want in the shopping and also anytime they finish an item (preferably when they open the last bottle/packet or know the stocks are low rather than when they've already run out).
Think bout what dinners are needed to deal with different activities - so a night when everyone is home at 5/6pm together might be a pre-prepared stew on the oven timer but a night with different activities at different times (sports, study, scouts, etc) might need a more flexible sauce for people to microwave and dole out as needed.