I use vinegar for light cleaning and dusting, and rubbing alcohol for almost all other household cleaning now. Isopropyl alcohol is basically magic — it sterilizes and completely evaporates with no lingering residue or fragrances. And a steam mop for the floor.
I put a white vinegar and water mixture into one of those inexpensive reusable spray bottles found in the cleaning aisle. If you need something a little stronger scrub with baking soda then squirt on vinegar, the two react together (base + acid) creating CO2 and further loosening grime as it bubbles.
I'd like rubbing alcohol, but the local supermarkets only sell it in the pharmacy and the bottles are a little small/expensive to use for cleaning ($2/ea for ish 500ml size).
Only chemical product I still use is toilet cleaner, since I've not found a safer alternative that actually works. Any suggestions there would be welcome.
Random pro-tip: They sell these spray bottles which release an ultra-fine mist. They're designed for hair/beauty but are absolutely fantastic for cleaning too. Just only put water in them as they're quite expensive relative to normal sprayers look up "Flairosol Mist Sprayer." You hand pump it a couple of times to compress, and then it mists like a deodorant. They're fantastic. Also great for hair.