set targetMessage to "Laptop logged in at" + timestamp
tell application "Messages"
set targetService to 1st service whose service type = iMessage
set targetBuddy to buddy targetBuddyPhone of targetService
send targetMessage to targetBuddy
error "Can’t make \"Laptop logged in at\" into type number." number -1700 from "Laptop logged in at" to number
You have a typo (actually a relic from other languages). Your first line should use an & to combine strings.
set targetMessage to "Laptop logged in at " & timestamp
The error message makes sense. It thought you were trying to add the string to the number, so coercing it to a number failed.