Most Chinese people dress for comfort, so you can plan to do the same. There's little risk of offending people with your dress: Westerners tend to attract attention regardless of their attire. Fashion capitals Hong Kong and Shanghai are the exceptions so opt for your smarter jeans or pants for sightseeing there.
Sturdy, comfortable walking shoes are a must: go for closed shoes over sandals, as dust, rain and toe-stomping crowds make them impractical. Northern Chinese summers are dusty and baking hot, so slacks, capris, and sturdy shorts are best. A raincoat, especially a light Goretex one or a fold-up poncho, is useful for an onset of rainy weather, especially in Southern China. During the harsh winters, thermal long johns and thick socks are a lifesaver—especially in low-star hotel rooms.
Keep packets of tissues and antibacterial hand wipes in your day pack. The brands in Chinese pharmacies are limited, so take adequate stocks of your potions and lotions, feminine-hygiene products (tampons are especially hard to find), and birth control.