Glass or ceramic is a MUST, imo.
yes, temp is a thing. The best time to start a culture is in the later winter/spring or early summer months, IME.
My sourdough cultures have always lived on the counters unless I was going to let them go dormant for a few weeks. Then, I'd refrigerate the culture at the back of the fridge where it wouldn't get disturbed/jostled, and I'd leave it be completely.
Then, I'd revive it in about a 24 hour period-- perform the split, feed, and then let it cycle once, split and cycle again.
You can select for a faster/slower yeast mix in your starter by 'forcing' it one direction or the other-- that is, if you feed and split on a shorter timescale, you'll select for more rapidly growing yeasts, and if you go longer, you'll select for those that multiply more slowly. On average, I mean. The upshot is that you can apply selective pressure (yay, Darwin!) so that you get a culture that raises breads the way YOU want it to work-- either a 6hr total time, or one that works overnight in the fridge or on the counter.