Hi shudderbug,
Can I check what you mean when you say "VPN browser"? There isn't a browser included with Avast Secureline VPN.
If you are referring to the Avast Secure Browser, you can change the page that is displayed when you first open the browser by clicking on the menu button in the top right corner (the one that looks like three dots in a vertical line) > click "Settings" > scroll down to "New Session" > select "Open a specific page or set of pages" > set the page you would like the browser to open to.
I'm afraid that it is not possible to change what page opens when you open a new tab or window (a search bar and tiles showing your recently visited sites will always appear), but you can change the page so that the search engine isn't Google. To do this, open the settings again, and change the "Search engine to be used in the address bar" to a different search engine.