Yeah, about 35-37 weeks is fine; my first baby was born at 37+6 and my second at 40 weeks exactly so I see no need to pack mine before then
As for what goes in it; literally just what you'd need to stay somewhere overnight - toiletries/deodorant/hairbrush/toothbrush and paste, spare change of clothes, socks, slippers, dressing gown, knickers, towel, nightclothes etc.
Then baby stuff for one or two nights - a couple of sleepsuits and vests/bodysuits, blanket (not essential though as hospitals have these, but I preferred to use my own), change of clothes for baby for going hom eif you wants, nappies, wipes/cotton wool, that kind of thing.
Then for labour and afterwards, maternity towels, breast pads, your own formula if you're not going to breastfeed, umm....any snacks/magazines you think you might need in labour, definitely your own drinks - I'm taking a couple of those big bottles of value water from the supermarket at 16p each, as although they'll be heavy, the hospital water jugs smelt mouldy both times I was in. Oh and disinfectant wipes/hand sanitiser as the bathrooms were less than spotless too.
Lol sorry for the essay!
ETA: cotton hats for baby too - you'll need a couple of those, as newborns lose most of their heat through their head.