Would you go for:

1) one the same size and resolution as your laptop, so everything looks the same?
2) one the same size but lower res?
3) one the same DPI so everything looks the same size, but the monitor itself is different?

got a 1920*1200 laptop and so is the monitor.

Only duplicate the laptop if it is decent res in the first place, so 1080P at minimum.

Personally I’d go for a 1080 just because they are much cheaper and easier to get. If you get one with HDMI they seem to hot swap much better, too.

It’s 1080p and 15.6″. No-one seems to make monitors in that configuration!

Same DPI is nice to have especially if screens are adjacent. My work desk puts a 22″ 1680×1050 monitor directly above my laptop’s 15″ 1600×900 one. Line up one side and the pointer goes straight from one to the other down that side, but it’s way off on the other.

Not a big thing, more of a little annoyance. I tend to be doing a different task on each monitor anyway.