To run at a certain time each day, make it a scheduled task.
If you want to copy all new files, you could use the archive attribute. That is, by not copying any file that does not have the archive attribute set. For that sort of thing, look at Robocopy. I would recommend using robocopy for any regular copy operations actually, especially if you want to exclude certain things. Check it out. /m does the archive thing
This is installed by default in newer versions of Windows. I think you can even just copy the executable over. The newer versions also have more options than the old version that came in the Resource Kit, I think.
I'm not sure how complex you want to get, such as determining the current date and then see if part of a file name matches that (rather than just looking at when the file was modified). I could probably do that if I had to with a batch file (using FOR and IF commands), but instead I'd really try to get PowerShell installed and do something more straightforward.