The Sibu Heritage Centre is the best first stop in town, especially if Sibu otherwise feels like a jumble of markets, shophouses, and river traffic. The displays cover the communities that shaped the lower Rajang: Iban, Malay, Melanau, and Foochow Chinese settlers, with costumes, tools, photographs, and domestic objects doing most of the explaining.
It is a modest local museum rather than a blockbuster, but it gives context that makes the rest of Sibu easier to read. Go before the market or temple walk, not after, and you will notice more in the streets.