I do most of my research of my family history in Bermuda and the rest of the world on the internet. I live in London, England now but I was born in Canada, so I can go to the Family centre over here and when I used to go home to Montreal, I used to try and get to different places to check my research. As I said, I mainly use the net and have met some wonderful people who have given me info that has been a godsend.
Like you, my paternal ancestors went to Bermuda in the early 1600s but I can only go back in dates to the early 1700s. My family surname is SMITH so thought I would have had a lot of problems finding them, but it was quite easy once we had my dads birth certificate with my grandfather's name on it with him being born in Bermuda.
In 1996 I bought a Familytree Maker CD and on it was my family (with a lot of mistakes) and since then I have been busy with the research, although I have given up a few times as I kept banging my head against a brickwall and getting nowhere. At the moment I'm just sorting out all the hints on Ancestry.com to see what I can add to my tree.
I have about 24/26 HARRIOTT surnames in my tree. The earliest one I have is; BENJAMIN HARRIOTT b: ABT 1730 married to MARY GILCHRIST b: ABT 1735. I also have a DAVID WILLIAMS in my family tree.
Guess that's it for now, but if you want more info about the HARRIOTT or WILLIAMS family let me know.