Do I need to worry about using a plunge router for edge work?
Not necessarily. Plunge routers can be difficult to use on edges, because their design tends to make them prone to tipping. Many plunge routers have a release that's used to change the depth of the router. For edge work, the best thing to do is lock the height in place
before you turn the machine on. At that point, you can treat it just as you would a fixed-base router. Of course, any router used for edge routing needs to be well-supported so that it can't tip over during the routing operation!
As spiffykyle mentioned, if you're going to buy a router there are many packages that contain both fixed and plunge bases. Look at the Bosch 1617, DeWalt 618, or similar. If you have a choice, I like a D-handle fixed base rather than a traditional two-knob design; better control. Also, if the only thing you're going to build is MAME cabinets, don't think you need a 2.25 or 3HP router. My most-used router is a small 8 amp, 1.5(?) horsepower model. The light weight makes it extremely easy to control, unlike my Bosch 1617.