apple ipad mini 2 stuck on itunes plug to usb port

Presumably your iPad indicates that it must be restored:

If you see the Restore screen on your iPhone, iPad, or iPod touch - Apple Support

These support pages outline the available methods to restore an iPad - either from a backup, or to Factory Settings:

Restore your iPhone, iPad or iPod touch from a backup – Apple Support

Restore your iPhone, iPad or iPod to factory settings – Apple Support

Restore all content to iPad from a backup - Apple Support

You’ll need access to either a Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS).

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Use of a PC or Mac computer is unavoidable. If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.

Genius Bar Reservation and Apple Support Options - Apple

The iTunes alert that you see concerning space refers to your computer having insufficient storage with which to download, unpack and verify the software package. Ensure that your computer’s primary/system partition has adequate free space.