The first and foremost step is to never buy cryptocurrency from centralized exchanges, that is where most of your privacy data gets leaked. Then we can use VPN or TOR to avoid our traces on internet but my suggestion is TOR since even most of the VPN tracks our data and sell them as well.
A bit extreme there with the craze of privacy. Honestly speaking you cannot be so anonymous that you can hide all your tracks - because if that was true then criminals would not be caught by FBI once a while and put in jail. Obviously they will make have left some tracks.
There is no harm in buying from a centralized exchange if that exchange operates from your country and you have been KYC-approved. If you are looking forward to launder money then this is not the case, in which case you will be caught one day.
The whole point of "remaining anon" with crypto started when some people wanted to use this freedom as fiefdom.
They dont wan to listen to the law and do as they wish, but trust me, majority of users here are law abiding ones - at least they sleep well at night knowing that they are not doing anything illegal.
As for what the OP said, Bitcoin itself is as we say pseudo-anon. There is no harm with that. Go with Monero if you are too conscious about privacy. But I would not spend money on it. Any group which advocates use of its system because is gives "more" privacy is likely feeding on your fear of being caught. Dont let that happen.