Custom spaces with external monitor
Solution 1:
in Spaces Preferences you can set the browser application to appear on all spaces. that's how i have my Terminal set up, among a few others. unless you move more apps onto your secondary monitor, the browser window should constanly stay visible even when switching around Spaces.
Solution 2:
This is a third party, non-free app, but it helps keep your applications organized across monitors and within Spaces as well. http://most-advantageous.com/optimal-layout/ (I am not the developer, just a happy customer.)