Which heating system (with hot water) would make sense in a tiny house?

I think has already shown the right option. A fan heater is inexpensive to purchase and also provides immediate warmth. And of course, an instant water heater.

Leaving electric heaters unattended in a garden shed always has a certain risk. If you want more luxury later, the test phase didn't cost much but was immediately and without modifications feasible.

For a well-insulated 20 square meters, I would take two 600-watt infrared panels. In the transition period, 600W should be enough, and if it's cold, you can turn on both.