If you want, post your web site URL here and I'd be glad to give you some feedback. I'm sure others will too.
Something to consider is a Genealogy Blog or Blog rather. I have one but its focus is Google Earth & Genealogy, not my personal family history. Do a search for Genealogy blogs and you might just like what you see. You won't need FP for it, sorry to say. I have FP 2003 as well and don't use it for publishing/creating web sites about Genealogy. Don't mean to burst your bubble, but FP may be near the best HTML/Web Site creator, but it’s just not for me when it comes to this subject.
If you want to see what I have done, and its $14 a month; it’s worth it to me. Or you can certainly try their free version.
As far as your other questions go...designer sites can be good, but you lose flexibility when trying/wanting to change things around. I do concur with Joe on his points.
You don't really break your existing site into pages....well, in a sense you may. This can be done by keeping each subject on a separate page. Like Joe is doing, as well as include a main menu with the primary subjects on it. This is where blogs come in handy, plus they are the NEW Web. Anyway, keeping each topic short with a link for more on a separate page is what keeps people reading your site content. Instead of having to read all the topic to get to the next then can choose if they are interested further and select a >>more<< link or something like that.
Let me know if I can help further and please do post your URL here for us to take a look.
My Blog is here >> http://apoetsblues.typepad.com/studentsofdescent/