I want to keep my passwords and those sites that Chrome suggests on the screen when I create a new tab. What settings should I use.
You need to use Custom Clean and untick 'Session' for Chrome, see the link below for more info:
If you are using Custom Clean and it is removing your <em>saved</em> passwords then also untick 'Saved Passwords' and 'Saved Form Information' (You should normally have those unticked anyway).
The page you are shown when you open a new tab is a setting in the browser itself, you can also get add-ons/extensions that give you more options of what is shown when you open a new tab.