Radar ensures robust sensing capabilities in adverse weather conditions, yet challenges remain due to its high inherent noise level. Existing radar odometry has overcome these challenges with strategies such as filtering spurious points, exploiting Doppler velocity, or integrating with inertial measurements. This paper presents two novel improvements beyond the existing radar-inertial odometry: ground-optimized noise filtering and continuous velocity preintegration. Despite the widespread use of ground planes in LiDAR odometry, imprecise ground point distributions of radar measurements cause naive plane fitting to fail. Unlike plane fitting in LiDAR, we introduce a zone-based uncertainty-aware ground modeling specifically designed for radar. Secondly, we note that radar velocity measurements can be better combined with IMU for a more accurate preintegration in radar-inertial odometry. Existing methods often ignore temporal discrepancies between radar and IMU by simplifying the complexities of asynchronous data streams with discretized propagation models. Tackling this issue, we leverage GP and formulate a continuous preintegration method for tightly integrating 3-DOF linear velocity with IMU, facilitating full 6-DOF motion directly from the raw measurements. Our approach demonstrates remarkable performance (less than 1% vertical drift) in public datasets with meticulous conditions, illustrating substantial improvement in elevation accuracy. The code will be released as open source for the community: https://github.com/wooseongY/Go-RIO.