I'm about to do a Cowboy character, and I was wondering where I can find a Brush Gun really early in the game (obviously accessible to me). Good revolver would be real nice too.

Gun runners a leveled list item, so nope.
NCR elite rangers with them only show up after a few quests after NV's factions MQ.
The NCR safe house may have one, but that will require as much work as the other options.

Pistols, any where after Mojave outpost you'll see some .44's spawn in random loot containers in caves if you scout around and take the risk.

I think brush guns only shows up in shops and on NPCs when your level is high enough. Can't recall finding anyone lying around in the world.

However,

This belongs in the Hints, Tips, and Spoilers section.

Earliest I found one was

Get Veronica (the 188), go to BOS compound.
Talk to the elder & accept quest.
Go to Armory.
Buy Brush gun / wait 3 days at a time until it randomly shows up for purchase.

I bought mine at level 4.

As for the revolver... max lockpick out of the gate.
Once you get 75 lockpick grab lucky from Prim.

Your standard .357 should suffice until you acquire Lucky and the Brush Gun.