The order isn't really relevant. It seems to have changed to such a complex sequence of changes as to which spot affects color or attribute or item type that unless you have a LOT of money to spend you should plan on reforging everything you want to make at least several times.
Triforge rearranges your 3 items into the possibilities available from what you put in. If you put in 3 skins getting a shirt isn't likely, you will get a skin. If you put in 3 red items getting a blue item isn't likely. If you want a white skin you need to put in at least 1 skin and 1 white item. Triforge it over and over and you will eventually get a white skin. Put in 2 white items or 2 skins and you won't have to redo it as many times because you decrease the number of other colors and item types that can come out.
Some items have multiple possibilities like red tiger. It has black, red and tiger pattern in it so you can end up with a few more possible results than if you just use a red skin or a black skin. When you mix patterns like tiger and ring dot you can get a lot more different results and it becomes less easy to predict. Unfortunately some of the best skins like lava and muscle require that you put in unpredictable skins like these.