The quickest and easiest way I have found to put a family history database online is this:
I ask PAF to generate a "webpage", then I move the website folder that PAF creates to my Dropbox's "Public" folder. I open the website folder and right-click on the index file, then from the Dropbox menu I copy the ULR. Dropbox automatically copies the website to their servers.
For example, here is a website that I created in about 10 miutes (I subsequently tweaked the index file to add a photo and change the layout sightly, but the original version generated by PAF was perfectly OK.) http://dl.dropbox.com/u/20318248/bill1847/index.htmhttp://dl.dropbox.com/u/20318248/bill1847/index.htm
This approach avoids the need to find a webhost, install and learn FTP software, and worry about rules that govern the size and number of files you can host, worry about the possible contents of advertizing banners, etc. My largest website is about 50MB, so a free 2GB Dropbox account might hold hundreds of large PAF websites.