Going by your weeks I take it that you are due sometime in July. If you read the antenatal 'Due July' thread you will find 2 ladies on there have already had their babies! Both before 31wks so I would get on with it as you never know. I remember most of us on that thread were dithering about when to pack but once one of them told us they had gone into labour we all leaped to packing asap.
As for me, I'm 33+2 today and I have packed 2 bags, one for baby and one for me. I haven't split mine into labour and afterwards bags as I don't want to end up with too many bags. Someone will have to carry all them. I can only imagine that for labour, I will wear one of the massive tshirts I see knocking about in our house, lip balm, fluids and snacks. The rest of the bag has my after birth stuff like pads, massive panties, towel, shower things and moisturising/deodorant things, dark nightie (no pyjamas just in case catheter, examined, etc need easy access), leggings and nursing top if reqd, 2 nursing dresses if I am in hospital longer than a couple of days.
To leave at home I have prepared a pile of things that we might need if we stay in hospital longer than a few days- nappies, pads, a few baby vests and gros, panties for me, a couple of outfits that are easy access for breastfeeding and pjs. Dh can bring these to the hospital if needed.
I have pinned a list of last minute things to pack last minute like the bottle if squash in the freezer to sip on while in labour, make up bag to do myself up when leaving hospital (won't bother if it's at night though), chargers, etc