The patient’s presentation of hemoptysis, weight loss, hoarseness, and a smoking history strongly suggests lung cancer, particularly involving the right upper lobe, which can compress the recurrent laryngeal nerve causing hoarseness. The best initial investigation is a chest X-ray to identify any obvious mass or lung abnormality, followed by a contrast-enhanced CT scan for detailed assessment of tumor size, local invasion, and nodal involvement. Early imaging is crucial for diagnosis and staging, guiding further management such as biopsy and surgery. Other options are less likely based on symptom combination and clinical findings.

Reference: Harrison’s Principles of Internal Medicine, Jameson et al., 20th Edition.