This paper investigates a finite horizon state estimation problem for a class of discrete-time stochastic systems with random transmission delays and out-of-order packets of data. Employing an event-driven signal-choosing scheme of logic zero-order-holder (LZOH), a system model is established synthetically in a unified form considering the network-induced phenomena, to drop out-of-order packets and improve system performance. By virtue of the established system model, a novel minimum error covariance matrix for the augmented state-space is obtained from the estimated variance constraint. With the aid of a finite horizon, the upper boundary of estimation error covariance is introduced during the information transmission from sensor to estimator, and the appropriate filter parameters are probed. To improve the estimation performance and alleviate the computation burden, an estimation-based compensation approach for random transmission delays is proposed using the received valid signals. Finally, the effectiveness and applicability of the proposed state estimation method are illustrated by a numerical simulation.