Without seeing pictures of your setup, I'd make a wild guess that they needed a ton more light. As an example, here's a popular light - https://www.amazon.com/MarsHydro-Spectrum-Hydroponic-Indoor-Growing/dp/B00XC3LBI2 - and it is advertised as being for a 2' x 2' growing area (though I think you could get more out of it than that, especially if you made some sort of grow tent equivalent. It's easy to underestimate just how much light plants need.
Growing from seeds will be more difficult and create lots of new hurdles to overcome, if you're still getting comfortable with plants I'd just pick up some seedlings.
However, you mention that you'll be a homeowner, so you might just consider growing your herbs outdoors. Not all of those herbs are perennial (basil is an annual, it will set seed which you can harvest but then it's gonna die), but you could also harvest and dry the herbs so you could have them in the off season if you cannot keep your cats away.
Another or additional option is to grow cat grass and catnip to distract the cats and give them something else to be excited about, and also give them vertical shelves away from your plants to play on or even a catio. Lots of times cats get into indoor plants because they are bored and need more stimulation. Plants and soil are full of interesting smells. Hope this helps.