At a high level, what you ask isn't hard, but there are some missing bits.
For example, you say "Attach PDF file to an outgoing e-mail". Where does this email come from? Have you already created the email and you're trying to add a PDF to it? Or do you want the script to make the email?
Also, you say you're looking for a 'quick action', this implies that you intend/expect to initiate this from the Finder, presumably by ctrl-clicking on the .PDF file and having the script respond.
Also, "Allow space for me to enter the recipient's address in the Automator/AppleScript"
What do you mean by this? Are you assuming the script will fill in the recipient's email address? Where do you expect this to come from?
As a starting point, this script added as part of a 'Run AppleScript' action should get you in the right direction, but as I said above, there are some gaps in understanding how you expect this to work.
on run {input, parameters}
set theFile to item 1 of input
tell application "System Events" to set theFileName to name of (get properties of theFile)
tell application "Mail"
set newMsg to make new outgoing message
tell newMsg
set subject to theFileName
make new attachment at end of attachments with properties {file name:theFile}
make new to recipient with properties {name:"John Smith", address:"johnsmith@nowhere.org"}
end tell
end tell
-- ask the Finder to move the file. Change the destination path as preferred
tell application "Finder"
move file theFile to (path to documents folder)
end tell
return input
end run
