Large language model (LLM) agents for web interfaces have advanced rapidly, yet open-source systems still lag behind proprietary agents. Bridging this gap is key to enabling customizable, efficient, and privacy-preserving agents. Two challenges hinder progress: the reproducibility issues in RL and LLM agent training, where results often depend on sensitive factors like seeds and decoding parameters, and the focus of prior work on single-step tasks, overlooking the complexities of web-based, multi-step decision-making. We address these gaps by providing a statistically driven study of training LLM agents for web tasks. Our two-stage pipeline combines imitation learning from a Llama 3.3 70B teacher with on-policy fine-tuning via Group Relative Policy Optimization (GRPO) on a Llama 3.1 8B student. Through 240 configuration sweeps and rigorous bootstrapping, we chart the first compute allocation curve for open-source LLM web agents. Our findings show that dedicating one-third of compute to teacher traces and the rest to RL improves MiniWoB++ success by 6 points and closes 60\% of the gap to GPT-4o on WorkArena, while cutting GPU costs by 45\%. We introduce a principled hyperparameter sensitivity analysis, offering actionable guidelines for robust and cost-effective agent training.