I joined GOG recently and I am looking to play older games from 90->2002 or so. But my laptop's screen size is small, its 13 inch.

Any one can comment how is the gaming experience of older games on a screen size like this? I remember back then a 17inch was gigantic so most games were made to be played on smaller sized screens.

In this particular case I am going to play Dungeon Keeper, a RTS game. Those usually need bigger screens.

If you can recommend a good external display within the price range of $130-200 that will help too for newer games from 2005

Games are fine on that size. I play mostly on a netbook with a 10" screen. Dungeon Keeper especially will be fine, if anything it'll be worse on larger screens as it doesn't support higher resolutions, so will look more pixellated or blurry (depending on how well the monitor scales).

As Gremmi said, pretty much every moniter should do fine. The compression rates and the scaling on moniters may change to accomidate what you're using them with but otherwise, for the most part you won't see much issue. If an issue does occur then there's a way to fix it without replacement, though it may take some figuring out.

For a lot of the non DOS box games here I never had an issue with eeepc and most games here. Although some like Ultima Underworld do chug a little more than I might like

Yeah, most old games will usually look better on smaller screens in their native (low) res, so you should be fine.