The key to accurate routing imho are the templates. I make an initial template from 6mm MDF and hand sand it to shape, which may be enough if you're doing some edge routing. If I need to plunge into the body, I'll use the thin template to make a thicker one.
There are lots of different types of router bits, but the useful ones here are the ones with a bearing fitted to either the top or bottom of the bit, that you use to follow the template.
I have had pretty good results with my little De Walt router. Any will do really as long as it has a standard 1/4" collet. A reasonable depth stop is essential for this kind of work and the ability to fit a side fence is handy.
Take great care though. Routers can be very dangerous tools. Make sure that your template won't slip (double sided tape). Practice on scrap wood first. Wear eye protection and a dust mask (MDF and lots of types of wood dust is harmful)