I live in <1000 sq ft with 2 kids and have scoured the internet for small space inspiration. The things that have worked for us include:
1. tall skinny ikea pax wardrobes. The tallest ones you can fit! We reach high shelves by stashing fold up step stools in the bedrooms, like these:
https://www.amazon.com/Greenco-Super-Strong-Foldable-Adults/dp/B00O9A57L4?ref_=ast_sto_dp
2. a reasonably attractive fold flat ladder, which we hang from a hook in nook in our hallway and actually get compliments on the look:
https://www.amazon.com/Hasegawa-Ladders-Lucano-Ladder-Orange/dp/B00GG65EYE?ref_=ast_sto_dp&th=1&psc=1
3. a storage platform in our bulkhead that rolls out for us to access (we have stairs in our unit going to the roof, but don't have access to the space beneath the stairs). Think something like this:
https://www.pinterest.com/pin/9148005497232564/ it holds all of our bulky things like suitcases, ski boots, etc.
4. vacuum sealed bags for out of season things, and for things like sleeping bags, extra bedding, etc that doesn't often get used.
5. drop down desks, expandable kitchen table that stores the expansion leaf when not in use
6. love these for shallow nooks:
https://www.pinterest.com/pin/629729960375098443/ They hold a lot! We have 4 as bins for our gloves, hats, sunscreen, bugspray etc by our front door, and have a couple in the kids room and elsewhere.
7. above-door shelves as I think someone else mentioned. Like this:
https://www.pinterest.com/pin/235031674281660866/
obviously purging constantly! As far as "stuff" goes, we fit nicely in our space. If we outgrow the space I assume it will be because all of the humans in the apartment are simply bigger. But for now, with a 5yo and a 3yo, it's working out better than expected!