Final answer:
The signs indicating arthritis in a client's wrists and hands are a limited range of motion and pain during movement, which are symptoms of rheumatoid arthritis, an autoimmune inflammatory disorder.
Step-by-step explanation:
When assessing a client's wrists and hands for arthritis, the finding that indicates the client might have this condition is A) Limited range of motion and pain during movement. These symptoms are consistent with the inflammation of synovial joints characteristic of arthritis, particularly rheumatoid arthritis (RA). RA is an autoimmune disease where immune cells attack the joint's synovium, leading to cartilage breakdown, joint swelling, and pain. The tingling sensation in fingers (option C) could point towards a different condition, such as carpal tunnel syndrome, and visible veins and warm skin texture (option D) are not typical diagnostic indicators of arthritis.