Webspace Managed Hosting

Hi, has anyone had to upgrade to broadband because the dial up connection is being discontinued? I am not getting much help from BT with help to my questions. At present with dial up I have free webspace, people know the web address and on search engines. On broadband free space is through geocities, who allocate the website name. What will happen to my old website and if I copy it to geocities will anyone find it if they do a search just using organisations name?
Hi,
not worried about cost. I’m concerned with the loss of my website and visitors to it. and not being able to keep the same domain name