A 55-year-old woman presents with pain in both finger joints for 2 years, intermittent and progressively worsening. Over the past 6 months, she developed knee joint pain, especially noticeable when climbing stairs. For the past month, she has had significant right knee joint swelling, limited mobility, and difficulty walking. Physical examination reveals distal interphalangeal joint bony hypertrophy with Heberden's nodes, right knee joint swelling with a positive patellar tap test (ballottement test), and obvious left knee crepitus. What is the first-choice diagnostic test for this patient?