I did this trip in October 2 years ago. You'll have your 'coolest' weather at the beginning of the trip in Beijing & Shanghai & the Yangtze, then it'll get steadily warmer the further south you go. Check the forecast for up to 2 weeks in advance on websites like Accuweather.com for the major cities you'll be in. Like many travelers, esp. in cooler weather, I bring layers of clothing (a tank top under a t-shirt under a 3/4 or long-sleeved shirt under a fleece jacket). My GCT fleece jacket was as warm as I needed, even on a chilly, damp, windy morning on the Great Wall (with my layers under it, of course). Do bring a well-fitting pair of walking sandals for Xian, Guilin and Hong Kong. I'd brought only walking SHOES, & my feet got very hot at the end of the trip (fortunately, I found some nice Rockport sandals on 50%-off sale in Hong Kong - wore them remainder of the trip, & still wear them in the summer). A good raincoat or poncho over your fleece also works as a 'windbreaker' on any damp, rainy or windy days, are very lightweight & don't take up much room.
China is a very 'casual' country - capris, jeans, chinos or khaki pants, polo shirts, and a couple of one-piece, short-sleeved pique-knit 'polo' dresses worked for me. Do bring a good sun hat & supportive, broken-in, walking shoes-sneakers, since at many sites you'll be on uneven pavement or stones (you do not need 'hiking boots'). I did not feel 'under-dressed' anywhere in China, even in Hong Kong.