How do I get rid of the safari start page on ipad?

That usually means Safari is crashing and closing all tabs or you're coming back after a set amount of time on which it is set to close all open tabs.

In the first case, something may be wrong with one of the tabs causing Safari to crash and close everything.

In the second case, you may have Safari set to close tabs after one day instead of letting them continue to exist for a longer period of time. Check Settings->Safari->Tabs->Close Tabs and make sure it's set to a period of time you like, or manually so it never closes anything unless you manually close it yourself.

In normal function Safari should open to the last tab you were on, and retain all other open tabs as well.

Safari will open to the last tab you were using. If you leave a tab open it will open to that instead of the start page.

If you close everything, then it will open to the start page.

You can create a shortcut on the Home Screen to open Safari too a specific page by tapping on the sharing icon

and then on Add to Home Screen from the menu that appears. Then every time you click that icon, it will open Safari to that page.

What's so irritating about the start page? Its your websites you visit or add as favorites? It's a convenient way to open things quickly.