Arbitrary-scale video super-resolution (AVSR) aims to enhance the resolution of video frames, potentially at various scaling factors, which presents several challenges regarding spatial detail reproduction, temporal consistency, and computational complexity. In this paper, we propose a strong baseline BasicAVSR for AVSR by integrating four key components: 1) adaptive multi-scale frequency priors generated from image Laplacian pyramids, 2) a flow-guided propagation unit to aggregate spatiotemporal information from adjacent frames, 3) a second-order motion compensation unit for more accurate spatial alignment of adjacent frames, and 4) a hyper-upsampling unit to generate scale-aware and content-independent upsampling kernels. To meet diverse application demands, we instantiate three propagation variants: (i) a unidirectional RNN unit for strictly online inference, (ii) a unidirectional RNN unit empowered with a limited lookahead that tolerates a small output delay, and (iii) a bidirectional RNN unit designed for offline tasks where computational resources are less constrained. Experimental results demonstrate the effectiveness and adaptability of our model across these different scenarios. Through extensive experiments, we show that BasicAVSR significantly outperforms existing methods in terms of super-resolution quality, generalization ability, and inference speed. Our work not only advances the state-of-the-art in AVSR but also extends its core components to multiple frameworks for diverse scenarios. The code is available at https://github.com/shangwei5/BasicAVSR.