A small kitchen is rarely short of storage. It is short of reachable storage. Things go in, and then they go behind other things, and from that point on the cupboard is decoration.
Everything below assumes you are renting. Nothing gets screwed to a wall, nothing gets replaced, and you can take all of it with you.
1. The drawer that will not close
Utensil drawers fail for a boring reason: nothing holds its position. Open the drawer and the whole contents shift forward, and eventually something stands up and jams the runner.
Fixed trays are the usual answer and they are a bad one, because you end up shopping for a tray that matches an odd drawer width and settling for one that leaves two inches of dead space at the side. An expandable divider avoids the whole problem. The YouCopia DrawerFit organizer widens to your drawer instead of you finding one that fits, which means no gap for a spatula handle to fall into.
2. Pans stacked into a tower
Stacking is what you do when there is nowhere else to put things, and it costs you every single time: to reach the fourth pan you lift three. Turning pans on their side converts a stack into a row, and a row is something you can see.
The Lodge 5-tier organizer does this in a base cabinet and holds lids in the same frame, so lids stop being a separate lost category. Cutting boards and baking sheets have exactly the same problem and the same solution, which is what the Fikoksol rack is for. It comes as a pair, so one goes in the kitchen and one usually ends up in the pantry.
3. The counter disappears while you wash up
A dish rack sized for a dinner party is a permanent obstacle in a kitchen with one metre of worktop. What you want is something that drains into the sink and gives the counter back when it is empty.
The KitchenAid compact rack has a drainboard angled into the sink, which matters more than it sounds: the alternative is a tray that fills up and then sits there. For the sponge and brush, which otherwise lie in a wet ring at the back of the sink, the OXO sinkware caddy keeps them upright and draining.
4 and 5. The two you notice later
Once the drawers and the counter are sorted, the two remaining complaints are usually the cabinet under the sink and the pantry. Those are big enough to deserve their own posts, so they have them: the cabinet with a pipe through the middle and seeing what you actually own.
Where to start
If you only do one thing, do the drawer. It takes ten minutes, it costs the least, and it is the surface you touch most often. Momentum in a small kitchen comes from fixing the thing that annoys you daily, not the thing that is objectively worst.