Dust first. No one is going to go over your furniture with a white glove, so do a good job, but don’t worry about every speck. Check corners for cobwebs and address those also.
Vacuum the upper levels first and work your way down. Move furniture as you go and put it back before moving on – this too eliminates duplicate trips back and forth.
Do a thorough clean of the bathrooms every week. Your toilet and sink may need some touchups throughout the week, but they should be cleaned top to bottom at least once every week. Thoroughly clean the grout and caulk of the shower and do the shower doors as well. Take everything out of the cabinets and drawers and sponge them out. Shake out the rugs, or better yet, toss them into the wash.
Your kitchen should also be cleaned once per week. Take the drip pans from the stove burners and clean them thoroughly. If you use your oven frequently, clean the inside of it also. Give some attention to your refrigerator and freezer – discard old foods items, and sponge out the inside of the refrigerator, including vegetable drawers. Do a thorough mop of the floor.
If you do your cleaning every week without fail, it will be easier each time