Firstly the circuit needs to be rcd protected (sensible to have it for the whole house but essential for outdoor circuits). You’ll need to use swa cable. Ideally it should be buried, but the rules say it needs to be protected from potential damage so that can be interpreted. Some are happy to clip it to a fence but that’s not ideal imo.
You can work out cable sizes here depending on your load: https://www.tlc-direct.co.uk/Technical/Charts/VoltageDrop.html You might get away with 2.5mm but probably worth going bigger as its a small part of the overall cost.
Lighting will need to be fused down from the power circuit but you can use a switch fuse which can double as a light switch.
Ideally run the swa all the way but it can he tricky to terminate. I’d probably run some twin and earth to a box then connect to the swa in there. You could use a waterproof box on the outside and run the twin and earth through the wall into the back of it.