I will offer that a good plunge router will be far more versatile than a square-chisel mortiser given you are just starting to gather tools. I have been doing Greene and Greene stuff for many years and have never owned a square-chisel mortiser. Just food for thought.
Try not to be overwhelmed by the info being delivered by fire hose :). There are a lot of elements to mission style stuff but, they are all basic; just repeated frequently. The same can be said for G&G; many basic steps yield your final result.
Attachment 428660
Here's a basic article on
making a frame and panel door. Your F&P sections would have flush surfaces and the grooves you originally mentioned are the gaps left to account for movement. The term crumb-catchers is accurate but, with a tablecloth on, all is good.
I would pick up some poplar, maple of whatever your local quality low priced wood is and do a couple of F&P mock ups. They can be smaller in size but, use the proper dimension thickness and width for the frame parts. This will introduce you to the process. I have made full mock ups of items out of construction lumber and scraps . . .
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. . . in this case I was testing the leg details and how I would lay in the breadboard splines. I still use these methods today so the learning holds its value. Of course they rapidly fall apart due to poor mixed material and movement issues but, that's what backyard fire pits are for. The point being that a prototype built from junk still takes you through the process before you get to the expensive material.
As to the router for mortising, I favor floating tenons when I am looking for ease of construction without sacrificing traditional joinery. I just grabbed the first one I saw and there may be better but,
here is a video on floating tenon joinery. I would use this on the F&P and on the apron to leg joinery.
Foremost, congrats on your desire to dive in to the project. I hope we can help you more as you go along.
P.s. For dark finishes, many products will get you there. Transtint Dark Mission Brown is great if you want to dye, Watco Dark Walnut or (darker) Black Walnut is good too. All would need a top coat.