I must fist say that the design pictures of your refugium are excellent. In looking at your refugium design I do see several issues. As pointed out by Bearjohnson, it's way too small for the size tank you plan to use it on. By the time you get all the baffles in it, and considering that you can only fill it about 3/4 full the amount of water in the refugium proper will only be about 8 gal. It is also a very complex design. Since your a cabinet maker, I do not doubt you can build it, but it will be a difficult thing to clean. That's a lot of surface area and a lot of small tight areas to work on for cleaning and maintenance.It's also a lot of points of failure. Over time joints fail, parts break and so on, and you'd need to tear down the entire refugium to do a decent repair.
I suggest you use two tanks with one for macro algae and the other for pod production. I would also only use one set of baffles. Baffles are installed to keep micro bubbles out of the system. You only need to do that for the return pump area. It's not an issue for water coming into the refugium, because it's not something you normally view. Another alternative would be to use one larger tank and combine the pod production and algae growing areas. The are not incompatible.
All this begs two additional questions -
What do you plan to keep in the main display tank? Depending upon what that is, you may or may not need a refugium to grow macro algae or to produce pods. No point in doing something that is not going to provide much benefit.
What is the rest of the filtration system going to be like? Generally a refugium alone is not enough to maintain a large tank.
As for sump size, it depends upon what you are planning to do with it. Usually you want it as big as possible, but you will need to allow for other factors. If you use a skimmer, you will need to decide if you want to mount it inside the sump or external to it. This will also apply to the return pump. Outside means the sump size much be reduced.
For flow through the filtration system, you want a minimum flow of about 5 to 10 times the main tank volume, so for a 125 gal tank the flow should be 600 to 1000 gph. Remember to account for head loss in the pump. It's quite a bit, especially with the powerhead type pumps. You will usually need additional circulation inside the tank. This can be done with circulation pumps inside the tank or closed loops. Yes, your going to have to add these even though you don't want the stuff in the tank. Planning is critical here. If you plan things properly, the pumps and/or tubes will be hidden. You will end up doing something for circulation, it's just a question if you will plan for it in advance. Your just not going to get the circulation you'll need from the filtration system alone.
Skimmer selection. Manufacturers tend to be "very optimistic" with their ratings. Choose one that is rated for a tank size about double what you have. Expect to spend some money on a quality product. Beyond that, most of the skimmers you'll be looking at for a tank that size, will work just fine.
To gravity feed a sump or refugium, you will need some for of overflow on the main tank. By far the best ones are installed internally and do require that you drill the tank. This is by far the best alternative, even though in your post you mention you don't want to do it. If you are going to use an external overflow box, I recommend getting one from Lifereef. They cost about twice as much as the "Brand X" ones sold by most of the online suppliers, but "Brand X" has a lot of inherent design defects that will lead to floods. See Lifereef here (offsite) -
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