Yes, a combination of Tumbling and Monero is a good step. I do this as part of my living. To bootstrap our company it took me over a month to get linked-bitcoins to unlinked-bitcoins.

Monero is not a magic-cure-all! Monero needs a very big warning like Tor Project says, how Tor is not alone going to save you.

Another big piece of management is a tree-shaped wallet-graph. You want to split your money regularly, then churn and obfuscate each wallet. And NEVER JOIN THEM. Even with Monero there is no safe way to join amounts. If you split into Wallet1 and Wallet2, then 10 transactions later they are running low and you want to consolidate, then you run a high risk of correlating all those transactions.

At this time, there is no official guidance on how to use Monero safely.