Proper leather shoes

Wood species isn't that important.

I read somewhere that the reason for cedar is actually an American thing as its a cheap wood in North America. It's "drying properties" were a later marketing addition.

Shoe brushes for the leather should be horse hair and boar/pig hair for the sole or bit in between the sole and upper.

Aliexpress is a good source. I got a shit looking one and then reshaped the handle and refinished it. It looks quite post now.

The little round ones like this are the most practical for application

and for off, just the biggest softest one you can find.

As above. Just remember what brush is for what colour, and what purpose. You want to use soft brushes for high polish shoes to avoid scratches, but you need a relatively firm bristle on the brush that you use solely for scrubbing dirt off.

I have different brushes:
Cleaning - brush off dried mud/debris
Apply polish (often this is actually a fine cotton rack or kitchen paper)
Buff

Those are all particular to the colour of the shoe - I don’t mix black and brown brushes. High polish dress shoes have a softer brush than brogued/durable shoes.

I do however use the same super large super soft brush for final buff polish, because it shouldn’t pick up any actual polish. If a brush is picking up polish then there is too much on the shoe, or you are brushing too hard.