Step nr. 1.: Assuming that your computer is compromised, reinstall the OS asap, install an antivirus and anti malware.
Paper wallet or hardware wallet.
If you want to buy and hold, you can use paper wallet, if you need to do transactions frequently your choise should be a hardware wallet.
If you want to maximize the security of the paper wallet, download a copy of a paper wallet generator, and install a fresh OS on a PC with a USB printer (without internet connection) and generate and print a paper wallet (or print at least 10 to be on the safe side).
If you don't reveal your private keys, your paper wallets will be fine to store the coins. You can use your public key to send coins to the wallets and you can check you balance without any risk.
This makes very much sense, using paper and hardware wallet. Thank you. However, reinstall OS, antivirus, anti-malware does not guarantee it can eliminate the unknown viruses/keyloggers 100% and also there are some virus/keylogger that can hide in storage MBR that you do not know about and connecting a new PC/equipment to your home network might get infected through your other equipment that is also connected to the same home network.
The best way to know this is if you use two factor authentication on as many things as you can have them on. Keep your twelve words safe, which is your lifeline if you are to ever lose your wallet on your phone. You can use them to restore onto any industry standard bitcoin wallet. Just remember to keep them safe and your passphrase as well if you used that to create a wallet.
2FA is not as secure if they already hacked and have access to your email without your knowledge and if your handphone is also hacked together, then they can re-route handphone text messages to the hacker first before it reaches you.
The better question would be: why would you not want to wipe your PC clean after knowing that it has been infected with something?
Format your hard drive and do a clean re-install. Secure it as you should. It it's your home network that has been compromised, use Tor or a VPN service when handling your coins. Bitcoin wouldn't be your only concern when operating from a compromised system either. Your PC could be used for DDoS attacks, your identity could be stolen, etc. The best thing you could do in this situation is wipe your PC. Everything else is risky.
Also, just so you know, typical keyloggers cannot steal your coins from desktop wallets for as long as you don't type out your private key or seed. They can't really do anything with your password unless you also use that password on online services elsewhere.
Even if you know your system is compromised and you wipe you PC clean, are you an expert enough of a person to trust that the PC is totally wiped out clean? What about viruses that can create hidden folders/directories in harddisk/usb storage MBR that a full format cannot remove them that you don't know about? Once you install the new OS, you would think the system is clean but in actual fact is not.
