What you need to have a look at is what's called often called CAGED;
http://www.premierguitar.com/articles/19390-7-the-guitarists-guide-to-the-caged-system
Simply put any barre chord is just a shifted open chord.
For instance, I'm going to guess that your Gm chord is barring the 3rd fret and doing an Em shape with the rest of your fingers.
Likewise if you keep the 3rd fret barred and do an A Minor shape, then the chord you'll be playing is a C minor.
A Minor(open) --> A# Minor (1st fret barre) --> B Minor (second fret barre) -- C Minor (third fret barre)
A way of learning the neck is take the G major chord.
Then learn all the variations you can do with it.
i.e. Open G, E Major shape, D major shape, C Major Shape, And G major shape barred on the 12th fret (if your guitar has enough fret space
)