Start with the versatile few
Space is your budget, so spend it on kit that does several jobs. A pair of adjustable or hex dumbbells cover presses, rows, squats, lunges and carries. A single kettlebell adds swings and goblet squats. A mat protects the floor (and downstairs neighbours) for anything done lying down.
That’s genuinely enough for a full-body programme. You can always add later, but most people never need to.
Think vertical for storage
The reason clutter kills a home gym is that kit on the floor becomes kit you trip over and resent. A compact vertical rack keeps dumbbells off the ground and turns a corner into a tidy training station rather than a hazard.
If a rack is a step too far, a sturdy storage box under the bed works - the point is that setting up and packing away should take seconds.
Buy for the flat you have
Adjustable dumbbells cost more up front than a single fixed pair, but they replace a whole rack of weights and take the footprint of one. In a small flat that trade-off is usually worth it.
Rubber-coated weights are also the quiet, floor-friendly choice - worth it when your gym shares a wall with the neighbours.
