Life is better if you can dust and vacuum on days when you can open the windows. I don't think people understand how much dust the vacuum cleaner doesn't pick up, not because it goes through the filter, but because it gets kicked up by the brush and never enters the fan at all. If you don't believe me, try vacuuming a particularly dirty carpet while barefoot.
Exchanging the air before the dust settles out is a lot better than having to dust a second time.
We've forgotten the unreasonable power of soap in our rush to Better Living Through Chemistry. Someone did tests and showed that a lot of 'cleaned' countertops are gross because the bacteria just get smeared around and homogenized, and counterintuitively the kitchen of a college student may be safer than the kitchen of a 40-something.
When I really clean my counters (parental visits, or realizing entropy is winning), I avoid a lot of cleaning products by first using one of those pot scrapers, then a little liquid soap, a scrub brush, and water. Once I've mopped that up the counter is probably clean, but if I use a cleaning product, this is when I do it. Just enough to swipe over everything, not to lift food particles or dried drops of tomato sauce from last night's spaghetti.
The other forgotten hero is white vinegar. They've tested removing pathogens, heavy metals and car exhaust from garden vegetables (turns out soil contamination is a surface exposure issue more than an absorption issue, even for lead) and white vinegar tested equal to or better than the best vegetable washes - which is to say that none are perfect but some are downright lousy.
Also make sure your sponges aren't gross. Using a gross sponge to clean things makes everything gross. Dipping them in white vinegar and some kettle water is a good way to clean a slightly funky sponge (and burn your fingers - patience is a virtue). Store your sponges elevated, or as I do in one case, prop it up against the wall so one edge (edge not side) is touching the wall and one touching the ground. And don't get sunk cost fallacy with your sponges. Buy in bulk, and when in doubt, throw it out. There's a kind of sponge that comes compressed, a dozen to a pack, and it expands the first time you get it wet. You can throw the spares in your junk drawer and they will get lost.
With plentiful, clean sponges, I tend to use a damp sponge when entropy is winning on the dust front (when it's so dusty you can see the dust from halfway across the room) because otherwise most of that is just going into the air and landing again. A wrung out sponge works wonders, and with a light enough touch I can even use it on books and banker's boxes without leaving any water damage. I recommend practicing on boxes, because if you squeeze the sponge, you might get a water spot. Cleaning dusty bookshelves has gone from an ordeal to just another chore because of this.