A 45-year-old man presents with a 10-year history of plaque psoriasis. Over the past 6 months, he has developed progressive pain and swelling in the distal interphalangeal joints of both hands, accompanied by morning stiffness lasting about one hour and a sausage-like swelling of his third finger. Physical examination reveals nail pitting and tenderness over multiple DIP joints without rheumatoid nodules. Plain radiographs demonstrate erosive changes with “pencil-in-cup” deformities. Laboratory studies show a negative rheumatoid factor and an elevated erythrocyte sedimentation rate. Which of the following is the most appropriate initial disease-modifying therapy for this patient?