The best time to start packing a hospital bag and all that mess? I'm 30 weeks Tuesday and my doctors are saying I'll have her around 37 weeks, hopefully.. maybe earlier. they told me I won't make it 40:(
I'd start now, because with me I kept adding stuff I forgot, so basically get it started, you'll be finished packing by the time you go to the hospital.
Diaper bag can be packed 2 3 weeks before your due date. Your clothes bag, I packed mine while I was having contractions, lol. You'll need things like change of clothes, toothbrush, hair brush, comfy shoes, socks, blankets, pony tail holders definitely, phone charger, things like that but they're pretty much things you use everyday so you can't really put them away. But it's up to you really, whatever makes you feel most comfortable! :)