I usually recommend not manipulating the clipboard via AppleScript - not because it can't be done (it can), but because there are usually better options.
In any case, since I don't know what you're ultimately trying to do...
tell application "iTunes"
if player state is playing then
set TA to artist of (get current track)
set TN to name of (get current track)
set the clipboard to TA & " - " & TN
The issue is assigning this to a key shortcut, which AppleScript can't do on its own.
Case #1 – Copy current track's "Artist Name - Track Title" to the clipboard by pressing shortcut.
Applescript + FastScripts do it but I don't want an extra app in Login Items.
Case #2 – Copy selected tracks' "Artist Name - Track Title" to the clipboard by pressing shortcut.
That's what I have in clipboard after pressing cmd + c (unnecessary info: album, duration, etc.)
Thats what I want in clipboard after pressing shortcut (e.g., alt + c or cmd + c if possible)