
Ropes, bands and a kettlebell
Rubber and nylon do not mind damp. Bands, battle ropes, a suspension trainer and a cast-iron kettlebell cover most of what you need and all fit in one box.

Training outdoors in a garden-sized footprint — the kit that survives being outside, and the surface to put it on.
A garden gym does not have to mean a converted shed and a rack of weights. For most people it means somewhere flat, a small amount of kit that stores in a box, and the fact that stepping outside is easier than driving to a gym.
The constraint is weather, not space. Everything below is chosen for that.

Almost nothing should actually stay outside. The realistic setup is a storage box that everything lives in, next to where you train.

Rubber and nylon do not mind damp. Bands, battle ropes, a suspension trainer and a cast-iron kettlebell cover most of what you need and all fit in one box.

Anything with bearings, foam or electronics — benches, treadmills, adjustable dumbbells. Outdoor damp destroys them faster than use does.

A ventilated storage bench keeps kit dry and within reach. Kit stored in the loft is kit you will not use. See the Storage Upgrade.

A gazebo or an awning takes you from "when it is dry" to "most of the year", which matters more than any piece of equipment.

In a British winter, both ends of the day are dark. See the Evening Upgrade.

An IP-rated Bluetooth speaker, and consideration for how close the neighbours are at seven in the morning.
Recover afterwards. The reason a lot of people put a gym and a hot tub or ice bath in the same garden is that they go together. Both are covered on the Wellness and Water Features page — including the safety points that matter.