Privacy-preserving machine learning has become an important long-term pursuit in this era of artificial intelligence (AI). Fully Homomorphic Encryption (FHE) is a uniquely promising solution, offering provable privacy and security guarantees. Unfortunately, computational cost is impeding its mass adoption. Modern solutions are up to six orders of magnitude slower than plaintext execution. Understanding and reducing this overhead is essential to the advancement of FHE, particularly as the underlying algorithms evolve rapidly. This paper presents a detailed characterization of OpenFHE, a comprehensive open-source library for FHE, with a particular focus on the CKKS scheme due to its significant potential for AI and machine learning applications. We introduce CryptOracle, a modular evaluation framework comprising (1) a benchmark suite, (2) a hardware profiler, and (3) a predictive performance model. The benchmark suite encompasses OpenFHE kernels at three abstraction levels: workloads, microbenchmarks, and primitives. The profiler is compatible with standard and user-specified security parameters. CryptOracle monitors application performance, captures microarchitectural events, and logs power and energy usage for AMD and Intel systems. These metrics are consumed by a modeling engine to estimate runtime and energy efficiency across different configuration scenarios, with error geomean of $-7.02\%\sim8.40\%$ for runtime and $-9.74\%\sim15.67\%$ for energy. CryptOracle is open source, fully modular, and serves as a shared platform to facilitate the collaborative advancements of applications, algorithms, software, and hardware in FHE. The CryptOracle code can be accessed at https://github.com/UnaryLab/CryptOracle.