Hold down both mouse buttons when you switch on the A1200 or so a soft reset to get the Early Boot Screen :-)
The A1200 should display as normal when you plug it into a monitor - as long as the monitor can handle the resolution that you have saved. The Amiga can be outputted to a tv and a monitor at the same time using the same monitor driver, so you should be able to get the monitor working no problems.
I have very limited experience getting the Amiga online, so I'll leave that for someone else to explain :-)
