In this paper, we focus on the scheduling problem in multi-channel wireless networks, e.g., the downlink of a single cell in fourth generation (4G) OFDM-based cellular networks. Our goal is to design efficient scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a recently developed scheduling policy, called Delay Weighted Matching (DWM), has been shown to be both rate-function delay-optimal (in the many-channel many-user asymptotic regime) and throughput-optimal (in general non-asymptotic setting), it has a high complexity O(n5), which makes it impractical for modern OFDM systems. To address this issue, we first develop a simple greedy policy called Delay-based Queue-Side-Greedy (D-QSG) with a lower complexity O(n3), and rigorously prove that D-QSG not only achieves throughput optimality, but also guarantees near-optimal rate-function-based delay performance. Specifically, the rate-function attained by DQSG for any fixed integer threshold b > 0, is no smaller than the maximum achievable rate-function by any scheduling policy for threshold b-1. Further, we develop another simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with an even lower complexity O(n2), and show that D-SSG achieves the same performance as D-QSG. Thus, we are able to achieve a dramatic reduction in complexity (from O(n5) of DWM to O(n2)) with a minimal drop in the delay performance. Finally, we conduct numerical simulations to validate our theoretical results in various scenarios. The simulation results show that our proposed greedy policies not only guarantee a near-optimal rate-function, but also empirically are virtually indistinguishable from the delay-optimal policy DWM.