This paper examines contract choice and pricing decisions in a dual-channel supply chain where a manufacturer sells products through both online direct sales and influencer live-streaming. We develop two Stackelberg game models—a pure commission contract and a commission-plus-service-fee contract—and derive equilibrium solutions via backward induction. We analyze how streamer influence, channel spillover effects, and service fee intensity shape channel pricing, streamer marketing effort, and supply chain profitability. Results show that stronger streamer influence significantly raises channel prices and streamer marketing effort. The commission-plus-service-fee contract outperforms the pure commission contract in motivating streamer effort and lifting channel prices, yet the service fee has an optimal range: an excessively high service fee reduces total supply chain profit. A positive channel spillover effect enhances the profits of all supply chain members and improves system performance. These findings offer theoretical and practical insights for contract design, pricing, and coordinated operations in live-stream e-commerce supply chains.