They actually suggest using natural bristle brushes. I haven't tried anything other than the brushes that came with the master paint set so I can't really verify it, but I've read of pretty mixed results from people trying cheaper brushes.
The Beginner Guide has served me well as a good starting point. The Master paint set is about $80 on Amazon but it has paint and brushes to get you started. Other stuff to consider if you don't already have it would be:
I don't know if the rack and screen are absolutely necessary but I certainly fine them useful.
Spending a bit of money will fix your problem.
What you need to do is buy this thing. And then put that inside of a small-ish wastebin. Something like this thing.
Then buy a big thing of turpenoid, like this for instance.
Finally you can buy this guy.
Then here's what you do. When you're ready to change paints, wipe your brush as well as you can with a paper towel. Then clean the brush off in the brush cleaning bucket (which has a screen inside of it, it's not just a bucket--very important). Your brush will be mostly soaked through with turnpenoid, and you then beat off the last bits of paint/turpenoid into the wastebin/rack combo you made.
If you spend this money up front, you will have very pleasant painting experience from now on.
You probably don't need the chip resin brush for either of those paintings, but it wouldn't hurt to own one. The master set comes with a #2 script liner so you don't really need to buy another one. It also comes with a 1" landscape but if you have the money to spare it's really convenient to have two 1" and 2" brushes so you don't have to constantly clean them. (one with the darker shadow color and one with the highlight color, usually).
The only thing I don't see on your list is the beater rack and a trash bin to set it in. The beater rack is what dries the brush, unless you paint in an area where you don't care about paint splattering and can just dry it on the eisel like bob does. It can also be bought in a combo pack that comes with the screen, bucket, and thinner.
There are also some colors that don't come with the master set that bob uses often. You can definitely get by with the colors in the set, but you may want to check the beginners guide and see if you want any other colors.