Generating my own private key (noob question)

Greetings r/bitcoin. Just discovered your community. I have read the FAQ and the guidelines. This is my first post. I believe this is the appropriate place for it, but please let me know if it should be directed elsewhere.

I am contemplating moving a small amount of my savings into bitcoin as a hedge against the stock market ($5K or so to start). I have conducted enough research to satisfy myself that I would like enter the bitcoin market. I am concerned, however, about what software to use and how to generate a private and public key. I would prefer the coldest storage available, approaching absolute zero if possible. To this end I would like to generate a truly randomized and secure set of private and public keys with as little third-party or software intervention as possible. Is this realistic and what is the best way to go about doing so? TYIA