Compression techniques such as quantization and low-rank approximation enable large language models (LLMs) to run on current edge hardware with limited computing power, but the key challenge lies in balancing the allocation of precision and low rank within a fixed memory limit. We propose a training-free framework, BALANCER, which achieves global budget allocation for mixed-precision quantization and low-rank correction through information-guided subspace matrices. BALANCER collects a small set of calibration signals—activation statistics, reference gradient magnitudes, and a diagonal curvature proxy—and converts them into information-guided subspace matrices. Instead of relying on coarse-grained layer-wise importance allocation, BALANCER transforms these signals into gain curves for each weight in the matrix singular subspace, allowing a principled greedy allocator to distribute compression bits and ranks across the entire model. On the LLaMA-3.1-8B model, with an average of 3.6 bits per parameter, BALANCER only increases the perplexity from 6.63 to 6.78 (+0.15), while reducing memory from 16 GB to 3.9 GB, and enabling the model to be deployed on edge GPUs such as the Jetson Orin Nano (8 GB).