Hi @martyjames,
I love a good fencing project so I'm glad to see this is the next on your list.
You might like to start by looking at How To Build a Fence, Installing Rails And Plinths For a Paling Fence and How To Install Fence Palings for some guidance on the process.
The above articles use standard fencing materials such as 100 x 100mm 2.4m H4 Treated Pine Posts, 70 x 35mm Outdoor Framing H3 Treated Pine as rails and 100 x 15mm 1.5m Fence Palings. These can be used in your application, but they will require sanding to achieve a clean finish like in your example.
Looking at your sketch, I don't see any vertical posts. You will need one on either end of the fence to support the rails and the subsequent palings. I'd suggest these posts are attached to the low block wall using a suitably sized stirrup such as these Pryda Post Anchor Bolt Down w Washer and galvanized dynabolts such as these Ramset 10 x 50mm Galvanised DynaBolts. You should also have the post on the house side of the wall bolted to the tall brick wall using suitably long dynabolts. This will give the fence much more rigidity.
As you will not be burying any timber in the ground, you can use H3 timber posts as opposed to H4. The benefit to this is they can come prefinished like these 88 x 88mm 2.4m H3 Treated Pine Posts. I suspect this is similar to what was used in your example.
You will then need to select materials for fence rails. My suggestion is H3 framing timber such as this 70 x 35mm H3 Outdoor Framing Pine. You should run a rail both at the top and bottom of the fence, notching them into the posts on the end so they are supported vertically by the post. Please note that the bottom rail should not be in contact with the block wall as this will increase its likelihood of rotting over time.
Once the rails are installed, the palings can be installed. I'd suggest either 100 x 15mm H3 Treated Pine Fence Palings or 100 x 15mm H3 Hardwood Fence Palings can be used overlapping each other to achieve this look.
After the palings are installed, you can use suitably sized timber such as this 90 x 42mm 3.6m F7 H3 Treated Pine Primed LOSP to cap the fence and achieve a look similar to the one you've provided.
Once your fence is built, some sanding will help give a nice clean look, but please be aware that H3 treatments for outdoor timber contain hazardous chemicals, including arsenic. So, if you decide to sand them, please ensure you wear a mask and notify your neighbours and family to steer clear of the area.
Let me know if you have any questions, I am more than happy to assist further.
Jacob
