I used Auto's abroad and collected from Charlotte, dropped at Savanah. There was only a couple of car hire desks at Savannah so you are a little limited in your choice if you book direct with teh rental company, you do still face the same problems as far as insurance is concerned if you choose to book direct, IMHO it's still cheaper to use an "all inclusive" consolidator like Auto's abroad. The seemed the cheapest when I checked recently but it's worth checking Holiday Autos as well.
It is a VERY easy drive from Savannah airport to HH, I would estimate 50-60 minutes drive time. The airport is just minutes from i-95 and HH is well signposted from I-95.