OK, the picture is clearer now. Keep in mind that many of us have not used dial-up connections for many years. And, of course, that makes us happier Internet users. I can't imagine having to use a slow dial-up connection again.
I'm not sure this will help but I suggest you try dialing to establish your Internet connection first, and then opening your browser. Then, see whether you can get the home page setting to stick by taking this approach to connecting every time you go online.
You could also call your provider about this. Most Internet service providers provide some level of tech support.
Edit:
Having a dialup connection anything I put in internet search box seems to call up my internet provider.
What is the point of putting a search phrase in your browser before you establish your Internet connection?