Monero
Monero uses Ring Confidential Transactions to improve privacy and security. By bundling the sending and receiving of public keys with older network transactions, a mixer is created that is capable of obfuscating addresses. On top of Ring Confidential Transactions, Monero makes use of ring signatures and Stealth addresses to hide both the sender and the receiver in a transaction.
I prefer Monero (XMR) to be my privacy altcoin. Monero already used by many peoples.
Monero is the most popular altcoin that have a cryptonight algorithm to mine.
You can mine it using your CPU.