I think the top 3 power tools for this hobby are cordless drill, jigsaw and a router.
I didn't know what a router was before I bought it. It turns out I use it all the time: T-molding, cutting holes in Lexan, routing CP's to mount custom controls, installing hinges, flush trimming laminate & Lexan, bevels & edge rounding and many other instances where something just didn't fit right. The router also comes in handy for other home projects.
Unless you are an artisan with a circular saw or hand plane, I doubt there is a good substitute for a router. Maybe you could use a Dremel, but I'd spend the money on a router.