Hi Teedycat and welcome from me, too.
If you intend to get exbatts, which are pretty docile and will have been used to confinement, you should plan for two square metres of run space minimum per bird. Some of the more feisty breeds do need more room than this, and with chickens more space is always better if you have it. Once hens have settled down in this new garden territory they tend not to fly out, and since yours probably won't have either enough feathers or enough strength in their wings to fly at first, I don't think very high fences are an issue from the point of view of them escaping. However, as Chris says protection from foxes is paramount as foxes are now common everywhere. If you can make them a nice run with weldmesh sides, and either the floor lined with weldmesh or the weldmesh dug in down the sides under the ground, they should be OK if you can also roof the run. Weldmesh roof will make the structure stronger and more foxproofing but a waterproof roof will prevent the run getting muddy and nasty, whatever you use on the floor. The oak will give shelter and shade but a lot of rain will drip off it, also leaves etc, and there is the possibility that wild birds will shed redmite down from their feathers if the run isn't roofed. I use clear corrugated plastic which is easy to cut and fix and lasts well if properly installed. There are lots of threads on here with pics of people's runs and coops. I'm a big fan of plastic coops as they are much easier to keep clean and seem to resist redmite better than wooden ones. Do avoid a coop with a small attached run if you can. Thousands of these are sold, usually they are made from cheap imported wood which isn't waterproof in winter, and the run sizes are far too small for the number of hens the coop will hold.