Hm-m-m-m... well... I'm not the best person to be replying to your post. (I have a brown thumb. Any plants I ever try to grow turn brown & die. My wife is the gardener in our household.) A couple of things I do know, though, are that herbs in particular need lots of sunlight to do well. Plus basil, in particular, needs warm temperatures in addition to sunlight. Even outside, if the temperature cools off for any significant stretch of time, basil will begin to fade.

I personally wouldn't bother trying to grow herbs indoors unless you have a window with lots of sunlight. And even then it can be a challenge to have them do well. At least that has been my experience. They tend to just get "leggy" & pretty scentless as well as flavorless. But then I live where it gets very cold & dry in the winter & there's not much sunlight. Since you live in L.A. perhaps having sufficient sunlight would not be a problem. Placing your herbs under a grow light might help if they do need a bit more. Misting them regularly will help too. Herbs don't typically need to be fertilized.

One other thing I know, with regard to house plants, is that more plants are killed by overwatering than by under watering. You can always give them a bit more water if they need it. But if you water them too much, you can't take it back out. (It's always best to use pots that have holes in the bottom for drainage.) You also don't want to fertilize plants during the winter. This just makes them grow leggy because there's typically not enough sunlight for them to produce lush foliage... again... at least not where I live. It's helpful to turn your plants regularly as well so they're exposed evenly to sunlight all the way around. I turn ours about an eighth of a turn daily.

As far as what kinds of plants to grow indoors, I think I would pretty-much rely on the staff at your garden center to tell you what plants might do well. I think the quintessential houseplant is the philodendron. Spider plants typically seem to always do well indoors too; also parlor palms. African violets are good. But they can be a bit tricky to grow I think. They're especially susceptible to over watering. I myself am partial to Christmas cactus for some unknown reason. They can also be easily over watered as well.

So that's pretty-much the sum-&-substance of what I know regarding growing plants indoors. Perhaps we have some other gardeners, here on PC, who will be able to provide more & better information.