Not sure what you mean by 'high quality' or 'Large LCD', but on the assumption that a high-end/enthusiast card, and a high resolution LCD (like the Dell 24-30")...
If you're gaming then yes you want a high end card to ensure good frame rates at the native resolution of the panel, anything outside of native is blurry and defeats the purpose of a high resolutions. For a large but lower resolution panel you have more grace of course.
But for 2D non-gaming like Tony mentions, there's less need for a high end card and an X1300 would be fine for most things.
And like he mentions in both 2D and 3D the lager the resolution the more VRAM you need, what defines and limits that need is the uses within 2D/3D, professional apps for both 2D and 3D can often be much more memory hogs than games, but in the consumer landscape games are usually the memory hog with high resolutions, high levels of AA and AF, and large/mega textures.
For gaming on a high resolution large panel LCD what you want most is native resolution with framerates usually above 30fps as a minimum (avg around 60+), and for most modern games that requires the top tier in gaming cards.