download it again
I don't use the App Store, but I've read that once you buy it, you can get it again at no additional cost. There are probably some rules about that though.
He's correct, if you purchase something from the Mac App Store you can download it again for free - IF it's still in the Mac App Store. Apple has been known to discontinue selling app or programs so once you delete the .dmg you're out of luck.
My suggestion is get friendly with Automator. It's extremely easy to have it sort for you. For example here would be a way to group all your install files into a single folder:
1) Open Automator - Select Application
2) go to Files & Folders
3) Drag Get Folder Contents into the right workpane
set your parameters to this
Search: Downloads
All of the following are true
File Extension - Contains dmg - Make sure you don't put ".dmg"
4) Drag Move Finders Items into work pane - Set your parameters to this
To: Other... (Click Downloads - New Folder) Make your new folder for all install files
Go to File - Save... Save it as an Application then double click it anytime you want to clean up that folder. You can definitely expand this by repeating steps 3-4 to drop everything into folders (Music, Videos, etc)
Additional - Setup this process to autorun.
1) Open iCal
2) Create a new event for when you'd like the Clean up process to run (for the sake of this example lets say midnight)
3) create a new event on midnight
4) under alarm select Open file - choose the file you just created in automator.
5) Set Repeat to once a week.
Voila you're messy download folder is never a problem again.