I would like to do a moderate hill walking (5-6 hours) in the Peak District, and camp as well. Which part(s) is suitable, for this activity?
I usually visit Peak District for rock climbing, so I can't offer any ready-made itineraries for walking. If I were to plan a walk myself though I would start from looking at a good map, and the Ordnance Survey Explorer series is usually the best, see: https://www.ordnancesurvey.co.uk/shop/explorer-map-the-peak-district-white-peak-area.html and https://www.ordnancesurvey.co.uk/shop/explorer-map-the-peak-district-dark-peak-area.html (I recommend the Dark Area). These maps include marked trails, pubs and campsites.
Luckily Bing has Ordnance Survey maps, so you can start from there, e.g. http://binged.it/1tkAPFe
As a side note, in busy periods (summer, nice weekends) I strongly recommend calling the campsite first and making sure they will have a place.
Try Edale. There are several campsites in the valley, and some great walking in all directions. These campsites are also a short walk from the train station.