You aren't going to be able to mine more than a few cents of Bitcoin a month without specialized hardware.
As mentioned, Monero is best for privacy.
If you must use Bitcoin specifically, one option is to "wash" whatever you buy by using an exchange that allows anonymous account creation, then converting it to XMR and back before using it. You can also find someone to trade with in person for cash. There at least used to be localbitcoin to help facilitate that, if that's even still a thing.
You aren't going to be able to mine more than a few cents of Bitcoin a month without specialized hardware.
As mentioned, Monero is best for privacy.
If you must use Bitcoin specifically, one option is to "wash" whatever you buy by using an exchange that allows anonymous account creation, then converting it to XMR and back before using it. You can also find someone to trade with in person for cash. There at least used to be localbitcoin to help facilitate that, if that's even still a thing.