Is there a setting somewhere that would stop Safari from opening my last-visited site whenever I start it up? I'd prefer it to open to a blank page and wait for me to choose a site. Desktop browsers have that option.
The only way to do this is to close the webpages before you shut down Safari. If you do this it will start with a blank page next time you start it up.
If you want Safari to open on a specific website each time you start it follow these screenshots.
Possibly, but it's in keeping with the nature of the iPad, and iOS in general, which is that apps are suspended in the state in which they were left. When I was new to iOS I kept wondering why I couldn't have a "home page" until I realized what the thinking was. That's why I put the icon on my home screen to take me straight to iPF, which is the site I use most often.