Recently I purchased a large number of coins on an exchange and began to proceed to send them to a private wallet. I had $5000 stolen within about 20 minutes of my first deposit. I had followed the same procedure I have used for years without incident, downloading an offline generator, booting a machine with TAILS, creating a paper wallet, and depositing to it. I had thought this was fairly secure but now reading up on it I see how wrong I was.

Now I have several thousands more in various coins I have recently purchased sitting on the exchange where I bought them, and I am terrified of attempting to get them off the exchange and into wallets without getting stolen.

As I understand it, it is likely that there is malware on my machine deep in the BIOS or something which was capable of stealing the keys as they were generated.

I am sorely tempted to leave the coins in the exchange, since that has 2FA protection and, after all, it's the process of moving them that seems to be the biggest security risk, but everyone seems to agree that's a bad idea and I do hate the thought that a 3rd party is in control anyway. Can I please be advised on how I can safely get my coins into secure wallets? Thanks.