All the big names (Alamo, Avis, Hertz, Dollar, Thrifty, etc.) are fine. Find the best rate and go with it!
A couple of notes for your Big Island trip: if you want to
really explore the Big Island, you might check out Harper Car and Truck rental:
http://www.harpershawaii.com.
They certainly, absolutely, and without question

won't be the cheapest, but they'll let you take their vehicles anywhere you care to go...Saddle Road, the top of Mauna Kea, pretty much anywhere.
Also, rates are often cheaper from Hilo (eastern side of the Big Island)...especially for the Jeeps.
Best regards and have a great trip,
GM