Welcome to SC and to the Hilton Head Island area. I don't live there but I visit the area several times a year and monitor public safety during my visits.
Beaufort County agencies use Palmetto 800 site 63 (Beaufort Simulcast) exclusively. Someone else was helpful in posting the specific frequencies from the database in post #2 above. You won't hear these agencies on any other sites, so you have to ensure that you have created a system with only this site enabled. If you monitor the Bluffton or Port Royal sites instead, you won't hear Beaufort County agencies.
While Site 63 is a simulcast site, I have found that I receive transmissions pretty well on HHI with scanners not optimized for simulcast reception. There is only a single site located on HHI which seems to minimize problems with simulcast distortion. Your location and antenna will play a big factor in your success using a Home Patrol II.
As noted, all Beaufort County Law Enforcement agencies are encrypted, so you won't hear BCSO, Beaufort PD, or Bluffton PD traffic at all. BC EMS Dispatch is often encrypted, and some FD tac channels are encrypted. However, HHIFR dispatch and tac channels are in the clear, as is BC Fire dispatch (which dispatches all county fire departments except for HHIFR). Bluffton FD, which covers most of the area of Beaufort County "South of Broad" other than Hilton Head Island itself, is also in the clear.
SCHP Dispatch is often carried on Site 63 also. But it's the only state agency you'll hear on Site 63. It hear other state agencies or statewide talkgroups (EMD, DHEC, DOT, DNR, medical helicopters, etc) you'll want to monitor one of the other sites such as Bluffton, Jasper or Port Royal. You'll hear different agencies on different sites, so monitor each one for a while to get a sense of which agencies are carried on each site. Tailor your radio programming to suit your interests.
I hope this information is helpful. If you have additional questions, feel free to ask.