I'm trying it out or the rest of the month, but my preliminary thoughts are:
Monday- Clean the kitchen and write the week's meal plan. This includes wiping down the fronts of the cabinets and surface cleaning the appliances. I'll clean the shelves in the fridge periodicly, but not weekly.
Tuesday- Clean both bathrooms.
Wednesday- Mop and vacuum the main floor. Vacuum upstairs at least every other week.
Thursday- Catch up on Laundry.
Friday- One to Three periodic tasks. I'll post those later.
Weekend- Grocery shop.
I know there are more tasks that would be ideal to do every week. But that would be getting too ambitious. For now, this is enough. And it'll keep the house presentably clean.