As of now, only Gemini and Uphold wallets are working with Brave. You would need to choose between these two and make an account there. Once you get verified and connect it with Brave, rewards will automatically be added to your wallet.
The moment you get these rewards in one of these wallets. You can transfer them to any of your local wallet.
Note: Check the regional support for these wallets before making an account. There have been many changes regarding this.
I am adding the links of the notice on the supported regions for both wallets. Go through this first.