This won't be helpful, but my choices depend on the art. I also like to take into consideration the planned placement of the art even though the purists say that shouldn't matter.

As for pieces that don't look good with white matting, sometimes using a colored mat next to the item and then a white mat will work because the white isn't right next to the art. There are also those mats with colored cores that create just enough separation to make the white work.

Our preference is to choose mats and frames that, ideally, will complement each piece individually. Unless we had a series or some closely related pieces, it wouldn't occur to us to consciously go for the kind of cohesive look you describe. However, to the extent that our taste iteself is cohesive, many framing jobs work well with each other, and many pieces are done in similar kinds of mats/frames.
Many of our frames are brown woods or gold. Most photographs are in black frames. I don't care much for silver, and the only silver frames we have are on an oil that had already been framed that way in the gallery and some photographs, also already framed.

What I can see in this room, which has mostly contemporary pieces with a modernist look....(1) Colored pencil piece done on a brown paper; mat is a tannish color; frame is brown wood. (2) Ink and watercolor (blacks and greys) on ivory paper; double mat - wide outer one in a very light brown and thin inner one in black, and white edge on outer mat shows; ornate antiquey gold frame; (3) and (4) two modernist prints, black on ivory paper; mats are a slightly darker ivory; frames are black wood, very simple; (5) oil on board, much chocolate brown in it; frame is dark brown with a thin gold strip.

If I look into the next room....oh never mind. There are 16 pieces of art there! However, four of the 16 are 15th c. manuscript leaves, done on parchment, and all four are matted and framed identically (ivory mats and ornate gold frames).

Sometimes we go for colored mats, e.g., some Japanese prints with many blues in them and/or of night scenes are in simple black frames but with blue mats.

I tend to use white or off-white matting always. Depends on the artwork and the room it's going in, sometimes. But I almost always use a simple black frame. I tend to change things around fairly often, and it's easier to move art from one room to another if art isn't framed to "match" a particular room. I find that a basic black frame (usually wood) works in any room and in most cases, works for any art. Not 100%, maybe, but close!

hobby Lobby when they have 50% off custom framing (like twice a month). I frame based on the photo/art, not the room.

Framed and matted according to the piece of art. The majority of what I have is matted with cream or white, but a few have colored mats. Also like a variety of frames, but nothing overly ornate.

Plain straight wood or black with a double mat, white with black inner mat with black core 1/16th of an inch reveal...
I have a few double white mat.
And I have some matted in green suede with a white inner mat.
To each his own, I don't want my framing to compete with the art.

I select mats and frames to make the art look good.

For mats, I have brown suede, deep teal suede, deep mauve, cream, black, and other colors. Many are double matted, and some have has the cut edge "tipped" in a color.

Most of the oils have a cream linen liner between art and frame, but the frames have nothing in common except they enhance the pictures.

I make my own art, and when it needs matting and glass covering with the frames, i take the piece and go to my framer, and play around with matts till I find something that looks good. I usually pick a co-ordinating color for the border mat, and then a light neutral for the wider piece. Then I go to Michaels when they have their 40 percent off frame sale!

I would say that I get a mat color that matches the art, but doesn't compete with it, but it would be something in the realm of neutral -- white, ivory, light tan, etc. For frames, I almost always will choose wood as opposed to black or white, although I love the idea of a gallery wall with black and white photos with all black frames and white mats. Or white frames with white mats. But for around the rest of the house, it's generally wood.

For the majority of my matting I like it with a natural or antique white mat and where the inner mat matches the frame color. As several of my prints are antique botanicals I find the antique white works better than a pure white as the pure white would make the pages look dirty and so, for the sake of being cohesive, I've stuck with the same antique white for all of my outer mats. In my DR I use gold frames with inner mica mats. Others I've done with a black inner mat and blakc frame. In my MBR I have a set of botanicals where I broke my rule and have a dark green inner mat which pulls from the green in the leaves and black frames. I alternatively considered using the orchid color of the flowers, but at that time I felt that would be more restrictive of my color scheme, though recently I've been slowly adding more touches of purple in the room and now wish I did. As my groupings are all sets I wouldn't mix and match between rooms. I just bought a combo mat today which is a dark gray outer, black inner and thin black frame. The artwork is a pencil sketch my DS did of the Eiffel Tower. I felt the additional black/gray really set it off more than white and a lot in his room is in varying shades of gray, black and greige. I also have a set of prints in the room with the black inner mat, white outer mat and black frame. I'm hoping it all will work--esp. as I have a matted and signed photograph from my deceased brother of his sailboat and that mat is also gray. I cannot ever change the mat since he wrote a dedication to me on it.