How do I get iTunes to sync properly given this circumstance?

Question

I have a 16GB Nano 5th Generation. Right now, I have more songs checked in my iTunes library than my iPod allows. I am currently going through each song and determining their worth and either keeping it checked or unchecking it. Obviously, it's a tedious process, but I'm one of those types of people.
Either way, the space on the library exceeds that on the iPod. I recently downloaded a bunch of new songs this weekend, so it's way over capacity now. I'm still unchecking songs, so theoretically, a couple more can fit on there each time I uncheck a song. However, iTunes only considers how much it would take to snc the entire library to the iPod. So the songs I unchecked stay on there until I free up enough space for every song.
I was wondering if there is a way to make iTunes sync as much as it can? I realize some songs would be left out due to space but I was wondering if it's possible to have it sync as many as it can rather than waiting for there to be enough space for every single item.
Thanks!
PS: I looked at the sync settings when the iPod was plugged in and it gave me the option to either "entire music library" or "selected playlists, artists, albums, and genres." I figured the latter option would fix it, but then it leads me into having to check which artists/genres I wanna keep. I'd rather just have iTunes sync what it can rather than have me fork through the list and determine whether it has enough.

Answer 1

The problem here is that iTunes wants to make sure that the songs that were purchased are sent to the same device that purchased them.  In this case, you would need to authorize your computer first.   This is as easy as opening iTunes, find "store" in the upper status bar, and select Authorize This Computer.   A dialogue will pop up asking for your iTunes ID and your password.  Enter the ID you purchased the songs with.  Afterwords, you should be able to sync the songs.