Step 1: Understanding the Concept:
In a benzylic alcohol the \(-\text{OH}\) is on an \(sp^3\) carbon directly attached to an aromatic ring. It is primary if that carbon is bonded to only one other carbon (the ring).
Step 2: Check (A):
\(\text{C}_6\text{H}_5\text{CH}_2\text{OH}\) is benzyl alcohol. The carbinol carbon is attached to the ring, two H and OH, so it is primary and benzylic.
Step 3: Check (B):
\(\text{C}_6\text{H}_5\text{CH}(\text{OH})\text{CH}_3\) is benzylic but the carbinol carbon bonds to two carbons, so it is secondary.
Step 4: Check (C) and (D):
(C) is a secondary allylic alcohol. (D) is allyl alcohol, a primary allylic alcohol. Neither has a benzene ring, so they are not benzylic.
Final Answer:
Benzyl alcohol is the primary benzylic alcohol, option (A).
\[ \boxed{\text{(A) } \text{C}_6\text{H}_5\text{CH}_2\text{OH}} \]