I looked into this years ago.
It's all well and good to have an external GPU, but from what I can remember you still need to connect the external GPU to a monitor, otherwise you will keep using your Laptops on-board graphics, it's not going to be a portable solution.
They're expensive, relatively slow and you're limited by how powerful a card can be and the bandwidth inter-connect is usually only PCI-E 1x 1.0/2.0 or less which can cause a bottleneck (Comparatively most new Desktop PC's run PCI-E 16x 3.0 now.)
Usually the better and more elegant solution is just to buy a new Laptop or build yourself a Desktop.
If you have a laptop that supports MXM or AXIOM form factor graphics cards, sure they can be upgraded, but they usually cost as much as the notebook is worth, if you can find one at all.
If you buy a laptop for gaming, expect it to be out-dated and slow for gaming in a few years, that's the nature of PC gaming I'm afraid.
Desktops have the advantage here as mostly it's just a case of dropping in a new card and you're back to playing at maximum settings and they're cheap to upgrade.
--::{PC Gaming Master Race}::--
