Even without these privacy-focused wallets, you can use an HD wallet, where "child addresses" derived from a never-directly-used root key cannot be connected by a third party, unless you do something to connect them, by e.g. transacting with coins from both wallets from the same IP or in the same transaction.
The CoinJoin paper details the level of anonymity that it can offer. I could cite it to you here, but I am not convinced that you would read it if I did.
