This paper defines and explores the design space for information extraction (IE) from layout-rich documents using large language models (LLMs). The three core challenges of layout-aware IE with LLMs are 1) data structuring, 2) model engagement, and 3) output refinement. Our study investigates the sub-problems and methods within these core challenges, such as input representation, chunking, prompting, selection of LLMs, and multimodal models. It examines the effect of different design choices through LayIE-LLM, a new, open-source, layout-aware IE test suite, benchmarking against traditional, fine-tuned IE models. The results on two IE datasets show that LLMs require adjustment of the IE pipeline to achieve competitive performance: the optimized configuration found with LayIE-LLM achieves 13.3–37.5 F1 points more than a general-practice baseline configuration using the same LLM. To find a well-working configuration, we develop a one-factor-at-a-time (OFAT) method that achieves near-optimal results. Our method is only 0.8–1.8 points lower than the best full factorial exploration with a fraction (~2.8%) of the required computation. Overall, we demonstrate that, if well-configured, general-purpose LLMs match the performance of specialized models, providing a cost-effective, finetuning-free alternative. Our test-suite is available at https://github.com/gayecolakoglu/LayIE-LLM