You've got a few hidden questions in there. First, welcome. Second, there are many alternatives to brush expense but typically $50 for a decent badger hair brush is money well spent. You can get a $12 brush at say Target or a departments store, like a Proraso brush, but you get what you pay for in the $50 range.

Any shaving mug will do.

Yea, some guys get razor burn initially when they are learning but generally straights are so smooth and only have one blade that I often don't use shaving cream at all. No burn whatsoever.

Getting a perfect shave though takes a long time to learn. For me eliminating razor burn was far more important. That happens very quickly, like 5th shave.