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The cheap nasty stuff is. The Omega 10048 is about as cheap as you can go and not have it scratchy.
I've not tried better bit I've tried worse.
Horse hair, I've heard, is quite soft. Haven't tried...

Look at Frank Shaving brushes (look on the bay or at Star Shaving). They're decently made. I have one in Best that cost me less than $30. It's a bit floppy but it's been my go-to brush since June....

I do about ten laps after shaving to make sure my edge is dry.
I do about 40 before each shave.

The other fellows have given sound advice. For the soaps and cremes they're a YMMV.
I suggest trying both. Not to mention that you can get glycerin based soaps. And triple milled French soaps....