..........to boldly go where no/few have gone before."
Well I'd buy one, I'm picking one up when I go into town in half an hour, $32 new for one 9.5" X 6.125" X 2" #2-243 in the Fedco lists. There is one that is perhaps large enough for what you want it's like 12" X 8" X 2" which is huge for a heater core.
I had to point that out as it would save a heck of a lot of work. But to answer your questions.
Aluminum fins on copper tubeing would be fine. Copper is however a better cooling agent for fins than alum. just harder to work with, much like with blocks. Depending on the heater core of radiator the fin count can run anywhere from 12 to as high as 24 from what I've read. More is better, Cathar used a core that had 22 or 24 per inch in his Big Arse rads he was making at one time. But CAthar was building a shroud onto a heater core he had bought. Problem is knowing the fin count before you buy, although that won't be a problem for you. If you can find oval shaped tubes that are 1/2 to 5/8" by 1/8 to 3/16" wide like those used in some rads at a custom shop I'd suggest you buy some of that tubing as the cooling would be far better than round tubes. Or if you could figure a way to flatten small round tubes down uniformly that would also work. But I have no idea where to get this done or to buy the flat tubes. I also have no good idea how you'll make the tanks, 2" cu pipe at each end with cuts holes for all the small tubes? A massive soldering job as well. This is about all I can think of in regards to making your own rad.
A long serpentine series of passes of a single tube in a rad the size of even a mini case will I'm sorry to say kill off your pumps flow. You could real quick have 25 ft. of 1/2" tubing and perhaps much more. Even the best pumps will be brought to their knees by that many feet of tube with so many 180 degree bends. So while tempting for ease of build don't go down this road. This is also why oil coolers faded from use fast, poor cooling for the restriction imposed.
Battery effect is from aluminum and copper in the same system in contact with the water. Strange as it may seem the water pulls off molecules of copper and Aluminum when contacting both in the system although anodizing of the Alum. and anti-corrosive additives in the water can pretty well stop this. This will turn your water dark, that is your warning.
There are a few custom rad makers that can make any rad you wish, but they are expensive. Still think the best idea is buy, not build. But hope these answers are of some help. If your project comes out well, and I hope it will, how about posting some picks.
BE