each time my mac mini starts up, imessages and acrobat reader windows pop up and then I have to x them out. How to stop this?

Instead of "x-ing them out", use Command-Q (⌘Q) to quit the apps. In this way they are shut down and will not reopen the next time you login or restart the Mac.

Also, you might check System Preferences > Users & Groups to make sure those apps are not listed under Login Items. If one or the other or both are listed, you can remove it by clicking the item then clicking the "–" button in the box below the listing.

Finally, when you Log Out of your user or Restart or Shut Down the Mac you may see a check box for "Reopen windows when logging back in". Make sure it is unchecked.