Open a terminal window in another screen on login
You can write an AppleScript with the following statements:

tell application "Terminal"
    activate
end tell

tell application "System Events"
    set position of first window of application process "Terminal" to {X_VALUE, Y_VALUE}
end tell


The first one launch the Terminal while the second one moves its window to the defined coordinates. Export the AppleScript as application and make it run automatically at startup.