How to force OS X Notes application to lose formatting when I paste text from clipboard?

While I do find Notes.app very useful, especially due to the iCloud integration with iOS counterpart apps, I am very annoyed about the text formatting used by the application.

I just want to be able to copy text from web pages and paste it as plain text in this application.

Is there any way to obtain this? Maybe some Clipboard manager that can work in background, or even another application that I can use to obtain this.

While I would like to keep bold and hyperlinks, I do not want to keep any fonts or sizes when I paste the text.

Note: the solution should be transparent — not requiring me to use extra steps for pasting, ⌘V only.

You can use OptionShift⌘-V to paste and match the current style. This removes all previous formatting, links, etc.

If you would like to make this the default action when pressing ⌘V, open System Preferences -> Keyboard -> Keyboard Shortcuts, and select Application Shortcuts from the list on the left. Then, hit + to make a new shortcut, select Notes.app from the dropdown list, enter Paste and Match Style exactly in the Menu Title box, then hit ⌘V with your cursor in the Keyboard Shortcut box. After hitting Add, you can flip back to Notes.app and click on the Edit menu to see that the shortcut has been reassigned.

You can select the text in Notes app, then Format -> Font -> Remove Style. Unfortunately there's no keyboard shortcut for that command :/