It's difficult to get traction on this question. It's not really clear what you've got to work with (no pictures, vague description) and it's not clear what you want to achieve. I have no idea what "with out being too flat yet too shiny" means. If you want to have a go at this, post some pictures.

How about laminated sheet glass? It is a modern look but I think could look great with soapstone. Large 18 inch rectified tile (cut so accurate and straight so that grout lines are minimal) You would only have 1 tile per 18 inches of countertop. This would be minimal grout. Slab marble Semi gloss paint (easier cleaning) Stainless steel sheeting (not sure with copper accents?) I only have a backsplash behind my range (marble mosaic). The rest of my kitchen is painted sheetrock (highly scrubbable BM Aura paint) with soapstone countertops. It has been 3 years and looks as good as new. Also, keep in mind that you don't have to rush the backspash. It is one of the few things that can easily be done at a later date. You can have your outlets set for sheetrock depth and just paint the walls while you figure it out. When you decide on a backsplash material, it is easy to add the outlet extenders to bring them to the proper depth. The outlet extenders come in different depths for different tile dpeths and take only a few minutes per outlet to install (You may need longer screws). I am going on 3 years and still can't decide on the rest of the backsplash. By the time I decide, it will be time to redo the rest of the kitchen again. Good luck!

"Is it stupid/unclassy to install brand new cabinets and put formica on top?" I don't think so, because we built a whole new house with a grand kitchen (IMO) and most of it has laminate (island has DIY wood, and we have stainless by the rangetop). I have always had excellent experiences with laminate and with all the other expenses for the house, realized that, for me, it wasn't necessary to spend that much money on counters. Granite has just never been one of my dreams or 'must have someday' things. As soon as I, basically, gave myself permission to be happy with laminate and not worry about whether it was right or classless to put it in a nice, new kitchen, I felt much more relaxed and content. Recently my sister sent me an ad for a good price on marble, which is kind of my dream surface, but when I thought about how I can drop stuff, slide my mixer, spill things, etc. on my laminate without giving it a second thought, I couldn't seriously think of changing it. Of course, marble would need to be babied more than I think black granite or soapstone would be, but I think you know what I mean. I don't think you really need to worry about either material you're considering, but you don't need to feel you 'have' to have stone, either. If it were me, I'd choose the soapstone, because like our stainless, some wear and patina is expected in the long run, so I wouldn't worry if it got a mark in it to get, perhaps, a head-start on the 'patina.' :-)

Formica Idealedge comes in ogee and bullnose. I have the ogee. There is a brown line where the counter top ends. Not in the run of the counter though. My pattern is Dolce Vita and has lots of movement in the pattern and unless your face is up against it you can't see the brown line. Now, yours is a lighter color so you might see yours more. I also like laminate for ease of care and durability. Unless they come out with something new, laminate is the only counter tops I would have. Just remember no hot pots or cutting on the counter top. Of course that is true of a lot of different types of counter tops. I had my last Formica counter top for 24 years and overall looked as good as the day I put it in when I sold the house.