Since HCV genome is not so big, you can try using the complete DNA sequence (around 10kb). But if you want to choose between genes, take a look to some literature, because some genes are not a good choice:
http://www.virologyj.com/content/3/1/103
Always combining genes (two or more) with different mutation rate gives beter results than using only one gene.
The choice depends from the specific aim; phylogenetic analysis is a big matter. Rearrangements, transmission from a common source, correlation between different isolates, genotype identification, and more... What your goal?
I agree that full genome analysis will provide a number of information, however it is not useful for epidemiological studies that necessitate a great number of samples. Provide better information on your aim and a better response you will obtain.