Try to find pictures on this site of what your monitor looks like stripped. The shape of the LCD will dictate what mounting options are available to you (for example, if you look at my
PLOG you'll see that I had edge connectors coming off one side, and couldn't simply build a "slot" to fit it into.)
An LCD sled is the safer way to go, since you can keep the LCD safely secured while you finish your box (with all that sawdust flying around, you won't want it there). You can use type-2 Silicon caulking to secure the panel to the frame -- either to the cut-down frame of the monitor or into a wooden frame of your own design (just keep the caulk off the screen!)
Keep searching through these forums... there's no one "best" way to mount the panel, but it helps to see how several others have done it and choose what's best for you.