Your script opens the Spotlight menu. The keyboard shortcut for opening the Spotlight window is command + option + space...
tell application "System Events" to keystroke space using {command down, option down}
UPDATE: Given your revised answer, I have composed a little script that should do what you want...
set the searchText to the text returned of (display dialog "Enter the name of an item you wish to search for in Spotlight:" default answer "")
tell application "System Events"
keystroke space using {command down}
keystroke the searchText
--[1]
end tell
You can do one of the following things at [1]:
Open the top hit:
keystroke return using {command down}
Move the selection to the first item in the next category:
keystroke (ASCII character 31) using {command down} --down arrow
Move the selection to the first item in the previous category:
keystroke (ASCII character 30) using {command down} --up arrow
Move the selection to the first item in the whole menu:
keystroke (ASCII character 31) using {control down}
Move the selection to the last item in the whole menu:
keystroke (ASCII character 30) using {control down}