If you want to truly live underground comfortably, you have to have a sim optimized to do it. For this challenge, you can choose to be a vampire or a normal sim/any other weird race. Make sure your sim either looks like s/he has seen too much sun for a lifetime or like s/he never HAS seen the sun. Be sure to have the Hates The Outdoors trait if your sim isn't a vampire. You can also choose the Green Thumb and Loner traits. These traits make life in total isolation underground seem a-ok.

At this point, you can either move into a pre-built house (if you suck at building like I do) or a grand spankin' new lot. All you really need is a normal-looking decoy house and a sweet bunker. If you do decide to buy a pre-built house you can sell the furniture for extra money. Less taxes are good too, right? So once you have your nice little decoy, it's time to build your basement! If you don't already know, basements are found in Build Mode. All you do is click and drag with the basement tool like you're building a room. Be sure to include stairs/a ladder/an elevator. You can also build multiple stories to your basement. All you have to do is build a basement in your basement. It's basementception. Furnishing the basement is simple, as all you need are the things a sim usually requires to not die. Size doesn't matter. You can build a 4-story castle for your basement. I DON'T CARE. It's your basement, is it not? Do as your heart desires. I do recommend plant pots from the supernatural expansion, though. If you have them. No hard feelings if you don't.

Once you go vault, you never go back. Unless you want to. You can do either. If you do choose to go outdoors, choose a hairstyle with a hat and obtain a job. If you do choose to never go outside, you can either paint, hack, or write books for a living. These jobs do need Artistic/Perfectionist, Computer Whiz, or Bookworm, respectively. Pick any one of them and get going. If it gets boring, try having yourself some vault babies! Chat on a computer, get some friends, marry one of them, and live happily ever after as a loving couple who don't need no sun.
UPDATE: I learned that the Into The Future carpet/grass patches can actually grow plants. So use those too.

Thanks for reading! If you have any questions or have any ideas, don't be shy! Sharing is caring, there's always room for improvements, all that good motivational stuff.

I heard you liked basements, so I built a basement in your basement.