I want to create an AVD to test apps on a Samsung Galaxy Note 2. I have checked similar questions, but they are intended for older AVD versions.
Which device should I use
Which device should I use?
Unless Samsung has some downloadable device definitions that you can use, you should define your own device that matches the Note II as closely as you can.
Should I set the target as "Android 2.3.3 - API Level 10"?
Only if for some reason you downgraded your Note II to Android 2.3.3. The Note II ships with Android 4.1 AFAIK.