To figure out how much paint to buy. Measure the gross surface area. (Dont subtract windows/doors, etc) and then divide by 400.
For example, a sidewall that is 20 feet long and 20 feet tall, is 400 square feet and would require 1 gallon per each coat.
Before you do any washing, scrape away any loose paint. The more time you do with prep work, the better your final job will be.
You can power wash the sidewalls if you are careful. Use a lower powered pressure washer and AIM DOWNWARD and KEEP THE WAND MOVING. The water coming out is under a lot of pressure and if you aren't careful, you can eat the wood away.
If the shakes aren't peeling, I would skip the power washer and just wash the sidewalls using regular hose pressure. But, be sure to use a good siding cleaner and scrub all the dirt off and rinse thoroughly.
Most people will paint the walls right away after powerwashing. What you want to do is to let the walls dry out. Give them a week or two before you start painting.
Also, consider staining and not painting the shakes. Unless of course the walls were painted before. Then, stick with paint.
Once the walls have dried, inspect the walls again for loose paint. Scrape as needed.
Now, look at the joints between the siding and doors/windows. Is the caulk in good shape? If not, remove the existing stuff and recaulk the joints. (Don't caulk over old caulk, it will just fail faster)
As for the actual painting process. Brush side to side, brushing into the wet edge. Do the butts (bottom edge of the shakes first and then the flat surface. You can also use a pad painter for shakes.
Or, rent a sprayer and spray the siding. I will be painting my newly resided house this spring and that is what I will be doing. I spray the paint on and then back brush the paint to make sure it is on smooth.
Plus, don't forget to prime. Especially any bare wood.
Finally, buy the bet paint you can afford. Behr from Depot is a good choice, but look at the latest Consumer Reports for what they suggest.