I'm afraid I have left out some information that would surely have altered the course of this discussion. For that, I apologize.
I have a Ridgid R22002 2hp router and a table. So that much I wouldn't have to purchase. I have the tools, all except for the proper bits, but I have never actually used them. I bought this particular router to use with a Maslow CNC that I never took out of the box. This Ridgid router is the one they recommend, so I coughed up the $169 to buy it.
https://www.homedepot.com/p/RIDGID-11-Amp-2-HP-1-2-in-Corded-Fixed-Base-Router-R22002/202739521
Also, before I posted this, I went to Lowes and spent a
half hour trying to find a flat 3/4" 10-inch wide board, thinking to glue two pieces side by side and then rout the grooves in the door. Thank you to whoever said it was NOT a solid piece door, regardless of appearances. The paint on the door concealed the joints of the boards. I
may have to go back and buy a wider board, if they have one that would cover the center piece without having to be glued together from two pieces.
So all I really need is a cope and stick router bit set, and because I'm only using it for one door, I'm fine with it being from Harbor Freight. Some of those pricier sets would indeed cost more than just buying the door already made.
One other consideration is that if I make the door myself, my girlfriend will think I'm great. If I just buy a door, especially with me having a router already, she's going to think I'm lazy. So I want to have a go at it. If I can't do it, then I'll admit defeat and buy the dang thing. Now that I can see the components of the door in my mind, I think I can do it.
Wish me luck! And thank you to all who have contributed to this discussion. Without your input, I would still be quite lost.