So if I buy BRX I can put them (after july 24th) in the Breakout wallet on my computer. leave it open and running to stake new BRK coins? is that right?
Yes that's right!
Of course your BRX has to achieve maturity after a transfer before they can stake. Transfers of BRX resets coinage.
Keep in mind that this is the last opportunity to acquire BRX. Any BRX from the pool of ~6.5M that is unsold will be provably burned, reducing the supply of BRX forever. No more BRX will ever be created and after the sale, the only way to acquire BRX will be in the after-market.