We present a novel learning framework to solve the transport-and-packing (TAP) problem in 3D. It constitutes a full solution pipeline from partial observations of input objects via RGBD sensing and recognition to final box placement, via robotic motion planning, to arrive at a compact packing in a target container. The technical core of our method is a neural network for TAP, trained via reinforcement learning (RL), to solve the NP-hard combinatorial optimization problem. Our network simultaneously selects an object to pack and determines the final packing location, based on a judicious encoding of the continuously evolving states of partially observed source objects and available spaces in the target container, using separate encoders both enabled with attention mechanisms. The encoded feature vectors are employed to compute the matching scores and feasibility masks of different pairings of box selection and available space configuration for packing strategy optimization. Extensive experiments, including ablation studies and physical packing execution by a real robot (Universal Robot UR5e), are conducted to evaluate our method in terms of its design choices, scalability, generalizability, and comparisons to baselines, including the most recent RL-based TAP solution. We also contribute the first benchmark for TAP which covers a variety of input settings and difficulty levels.