What is the proper setup to cut straight openings with a router?
If you are willing to invest into expand your routers capacity, I suggest getting a set of router guide bushings. Sometimes they are specific to the make of the router There are videos on YouTube on how to use them. The bushings will allow you to make a template of the cutout you need whether it be  out of one large scrap piece or several small pieces fasteng to make a 4 sided guide. Its size is determined by the off set of the guide bushing to the router bit. If the OD of the guide is 3/4" and the bit is 1/4", the template is made larger than the top you wish to drop in by 1/4". You can start out with a guide to do the smaller hole first, (larger difference in the offset) for example the 3/4" guide and the 1/4" bit, and make the cut all the way through. Swap it out to a smaller guide (1/2" guide) and make the stepped cut to rest the table in its' place. 

Planning all this out is done with the finish in mind. Make a test cut using the smallest offset on a scrap piece of flat stock using another 4 pieces of smaller scrap to use as the guides. These pieces should be at least half the width of the router base. When assembled together it will more or less be a smaller example of the larger version you wish to do. This will let you get the feel of the router doing its' job and let you see in real time the offset the guide provides, enabling you to determine the placement of the templates for the cuts that matter.

Remember the test cuts are for the finish size to allow your top to drop in, the stepped cut. Before you start cutting on the actual piece after you determine the proper placement of the template, swap out the bushing to the larger offset, make the cut all the way through, then swap the guide back out to the smaller offset to make the final cut that allows the inset top to set flush.