Precision agriculture sensing technologies offer new opportunities for crop monitoring and farming strategy enhancement. However, limited connectivity in rural areas makes sensor data collection challenging. Unmanned Aerial Vehicles (UAVs) have emerged as an efficient alternative for data acquisition in agriculture. Prior research focused on optimizing system performance metrics like energy and flight time, while overlooking the operational costs demanded from farmers, a significant barrier to adopting precision agriculture technologies. This work proposes a novel UAV-assisted agricultural data collection framework for high-precision crop monitoring while reducing UAV operation costs. Specifically, we formulate an Optimal Sensor Set Selection Problem (OSSP) and demonstrate it is NP-Hard. We design an efficient heuristic algorithm called Cost and infeRence Optimization Process (CROP), which exploits data correlation to select the most informative set of sensors within the farmers' budgets. Data collected from these sensors are then utilized to estimate the measurements from unobserved sensors, providing an accurate view of the entire field. We validate our methodology through extensive experiments using a sensor-UAV testbed. Results show that our approach reduces the estimation error up to four times and requires 30% less budget to achieve near-zero inference error, compared to two existing methods.