When I am working out a stair configuration and basic structural considerations, I find that is it helpful to have a concept of what I want the final stair to look like. This might take a half hour longer during the early design, but it can save you hours of changes later. There are four components of a stair that need consideration - Stringers, Hand Rails, Guards, Treads/Risers.
The reasons that you might consider one material instead of another was covered in the 'Technical Rule Of Thumb' noted above. 99% of the time I use steel for the stringers. If I want the stair to be a focal point or a design feature, I discard the usual channel stringer solution and start to consider using a plate, a tube or a pair of boxed channels. I like the way these structural shapes look. You will need to get your structural engineer involved at some point, but there are lots of ways to get the look you want by varying the structural characteristics of the steel stringer. For instance, a standard 12" steel channel could be doubled up to form a crisp box shape about 3" x 12".
Usually getting the shape you want "overdoes" the structural capacity, as long as you stay close to a 12" depth or more. This same stringer could also be a 2" or 3" x 12" tube or a 1-3/4" x 12" box shape formed by welding a plate to close the open side of a channel. Or keep it really simple with a 3/4" x 12" plate. In all these solutions a key to looking good is to remove (grind off) all mill marks, grind welds smooth, and fill any joints by continuous welding or by using body filler.
Code has lots to say about hand rails, limiting diameter, shape and clearances. Hand rails can be wood, steel, aluminum, stainless steel, or nylon-covered metal. I think wood looks a bit out of place unless your building has a lot of wood trim elsewhere. Steel needs to be painted and the paint rarely stays intact for more than a month. I tend to use a lot of anodized aluminum for hand rails with a hairline jointing system. Stainless steel usually costs more and is harder to get and keep a good finish on. Nylon-covered metal is fairly expensive, but it is the only way to realistically introduce color. I don't like to leave the hand rail mounting brackets up to the contractor's discretion. The wrong brackets will "kill" a lot of design effort.
Guards are another item that the code controls by dictating configuration: height, strength, openness, climb-ability. The choices are pickets, screens, panels, glass, and solid. Before the latest International Building Code was released, which I haven't reviewed yet, the non-climb-ability provision eliminated everyone's favorite solutions - the horizontal rails, cables. This eliminated a lot of descent-looking solutions that weren't terribly expensive. You are left with pickets at 4" on center or jump right into some fairly expensive screens or panels. The screens are made of wire or expanded metal lathe in frames that are made to the sizes needed to fill the guard openings between posts and rails. Panels are similar except mostly solid and made from wood, composites or sheet metal.
The next big jump in cost is to glass. The tempered glass is expensive, and some of the stainless steel posts can take your breath away. Of course you can always put your own system together using epoxy painted steel posts and standard fittings to hold the glass. Unfortunately this usually shifts the cost out of construction and into design where you might not be compensated for your effort to save money. Solid guards are a low-cost solution. You need a steel framework into which to set metal studs and drywall. This solution works best when you can create an interesting shape out of the stair or you just want something without the curse of pickets.
The typical commercial stair has treads and risers made of concrete-filled steel pans. Code may also dictate 'closed' risers. How to dress this up? Rubber and vinyl are the only products that I can think of that are designed to solve this issue. Unfortunately, they don't really offer an up-graded appearance. They are the 'picket-solution' of tread finishes.
Carpet is the old standby and works well. Wood, stone, tile, and other floor finishes need some careful attention. The leading edge of the tread is very susceptible to impact damage or becoming a tripping hazard. Another issue is that a flooring over 1/4" in thickness starts to impact the stair configuration itself and may need adjusted riser heights at the top and bottom. That said, a 1" stone tread is well worth the attention to detail.
If you have gotten this far, you probably fall into one of two camps. First, those folks who can't wait to get their hands on the next stair design. Second, those folks who are sure they don't want to design a stair. I like stair design. It is like a mini-project with all the same considerations as a building without the pesky need to integrate the M/E disciplines.