With my first LO, I had my bag packed and in the car at 35 weeks because that's when the hospital won't make an attempt to stop labor. Before then, I could have had my partner go home or to the Wal-Mart across the street to grab the things I needed. My LO was born at 38w3d.
Also, since I'm in the US, all I needed was clothing for myself (and partner), a going home outfit for baby, and whatever grooming supplies I needed. Diapers, wipes, formula, clothes for inside the hospital, blankets, hats, etc. is all supplied by the hospital and covered by my insurance... most of the US works this way. Check with your insurance company and/or doctor/hospital.