I'm 37 weeks tomorrow and they checked for dilation for the first time yesterday. I've had my bag packed for forever though just because it made me feel more ready. Just whatever you need to make you feel more comfortable and prepared.
My midwives never checked me for dilation until I was admitted to the birthing center 13 hours into labor and I asked them for an update. It's really not necessary until you're in active labor because it doesn't tell you anything. You can be 2-3 cm dilated for 6 weeks or you can go from 0-10 in 4 hours. Checking early just raises your risk or introducing foreign bacteria and getting and infection - yuck.
Pack your bags anytime you feel like it, usually I see people do that and install carseat at about 36 weeks or so. Have a licensed safety tech teach you how to properly install your carseat - it looks easy but at least 80% of seats are incorrectly secured so there are some tricks to learn. It's good to know how especially if you will frequently be switching one seat between different vehicles.