Don't ever delete stuff from your main iTunes library, just to delete them from the iPod. You can set up iTunes to sync separately and differently to each device.
The latest iTunes may hide the sidebar. To show it, from the menu bar, under View, select Show Sidebar. The sidebar shows the iPod, under DEVICES.
How you remove songs from the iPod depends on how you have been loading songs, manually (by dragging songs to iPod) or by automatic syncing (by setting up the iPod's Music tab). If you need more information, please post back with the method you are using to load the iPod.
For reference, here is a general document about syncing to iPod
Showing the sidebar makes it easier for me to describe things, although you can do everything using the "new look" iTunes.
You can also pick and choose using automatic syncing. Here is one easy and convenient way to set it up.
Create a new playlist in iTunes. Put ALL the songs you want on the iPod on that playlist (up to the capacity limit of iPod). Select the iPod in the sidebar, and go to its Music tab (next to Summary). Set it to Sync Music, and below that, based on Selected playlists, artists, albums, and genres. Below that, under Playlists, checkmark only that ONE playlist. Click Apply to sync the songs on that playlist to your iPod. NOTE: Songs currently on the iPod will be replaced by the selection on the Music tab.
Going forward, whenever you want to update the songs on the iPod, just update that playlist (add and remove songs). The iPod does not need to be connected. The next time you connect the iPod (or when you click Sync), all changes sync automatically.
If you need to do a Restore, or you get a new iPod, you can easily make it just like before, by selecting that same playlist for syncing on the Music tab.