All sounds ok.
The actual route doesnt get too muddy at this time time of year: the ground on the south downs is pretty much hardpack at the moment.
A good idea for a B+B is the YHA at Truleigh Hill which is at about 60-65miles in and slap bang on the SDW which has been used by a few of my mates who did this last year, otherwise there are some B+B options in Arundel, Steyning Worthing, etc. cant recommend any from presonal experience though.
Kit? yup, loads of tubes patches or fit slime tubes to your tyres.
Food, well on the SDW the first food point fron Winchester is probably around Exton (Pub), then the QECP visitor centre which has a cafe, the next is the pubs and teas rooms at Amberley, Pub at Washington (slight detour), pubs and tea rooms at Steyning (slight detour), Pub at Devils Dyke, then its pretty much no food till past Lewes and then its all off the track.
If your camelbak takes three litres of water then thats good, an extra bottle is a good idea too as the taps on the route are not always working