While there is very little accommodation in the immediate neighbourhood of the walk HQ, there is ample in Weymouth. There are a huge number of hotels and B&Bs to service the holiday trade - more than 20 hotels, 150 B&Bs, a range of campsites, and 300 caravans and cottages. The HQ for the 100 is about 2.5 miles north of Weymouth town centre, with regular bus and train services from Weymouth to HQ, so Weymouth would be a good choice. Obviously, Weymouth will be crowded for the Bank Holiday and start of half term, so you will need to book early if you want a particular place. However, you could still expect to find somewhere with a month to go. Don't expect a bargain though.
You could also consider Dorchester, or, a little further out, Poole and Bournemouth, both of which are within easy reach of Upwey station next to HQ. In addition there are cottages scattered round the Dorset countryside.
If you have a camper van, you will not be able to park it at the School on the Friday night. You will have to organise somewhere else.
Because of the huge choice, we do not intend to recommend particular options.
For camping, Higher Moor Farm campsite is the closest at just over a mile away from HQ. You can also camp at Blagdon Fruit Farm GR SY658816 which is about 1.4 miles away from HQ. The main concentration of nearby and easily accessible campsites are around Chickerell: principally Bagwell Farm, Sea Barn Farm and East Fleet about 4 miles away and West Fleet about 6 miles away from HQ and in Preston: Seaview Holiday Park
There is camping at Ansty which is convenient for that part of Dorset and next to the checkpoint.