Because it is the whitest wood I can find I typically use aspen. It provides very good contrast. It is also inexpensive which is a plus if things don't go well.
But it does have drawbacks. For one it is quite soft which, in addition to limiting detail somewhat, it often leaves behind a lot of fuzzies that have to be dealt with before pouring the epoxy. The other big drawback is that it is quite porous so stains and paint bleed quite easily. I found that staining and sealing the wood before I start is the best defense against unwanted stain encroaching into the photo.
Maple works well too and because it is harder you can get finer detail out of it. It leaves behind a nice clean surface, free of fuzz and is not so prone to bleeding. The main caveat is that sometimes you get some "curly" maple effect which can detract from the appearance of the photo. With that said, I have had the curly maple effect kind of enhance the photo a bit too.
I have not tried birch but I suspect it works on par with maple with regard to machining characteristics. I don't have a good source for it is the main reason I have not tried it. Although I could try Baltic birch plywood I suppose. If it does work it would be very economical for sure.
One bit of advise to get the best results from any project on your CNC is to dial in your finish tools with a dial indicator. I almost never allow more than .001'' total indicated run out with any finish tool. If the tool is swirling around like a swizzle stick on the surface of your work it can't use its cutting geometry to very good effect.