From personal experience I would always recommend a two monitor setup so you can have your code/design open on one screen and the site you are working on on the other - this will be a real time saver.
Two monitors are certainly better than one, but I suggest, and use, three (plus a smartphone). Three screens allow:
a) A separate screen for code.
b) A full HD (1080p) display, to ensure that your layout does not "fall apart" on a large screen.
c) A 1366x768 display, to ensure that your layout works well with only 768px height.
It is quite common for web pages designed on and for 1080p displays to need to be scrolled up to show vital input fields on a 768px high display. This is, at best, annoying and often could have been avoided if the designers had tested their design on a 768px screen.
Incidentally,there are a number of screen emulators that allow you to check your design on a range of displays. I wrote one myself before I had multiple screens. However, they are not as convenient as having actual screens to test with.