How can I set up my iPad so I don't have to type in my password every time I try to download an app?
You can only remove password authorization for free apps. You can set it so it only asks for it after 15 minutes on paid apps, that is, if you purchased one, it will only ask you for your password if more than 15 minutes have passed when you try to buy a second one. 

This restriction does not apply for Apple TV.

Check this Apple Support document for further information: Manage your iTunes Store and App Store password preferences