Stainless steel is used to be the most common material for case. The High end watch is often made of Platinum or Titanium.
Platinum is a very heavy metal, and gives a shiny white metallic appearance. Unlike gold, pure platinum is fairly hard and resistant to scratches (similar to hard stainless steel). For this reason, it is often used in 95% purity (i.e. Pt 950). However, raw platinum is expensive to be used, not only because of its rarity, it is tough and the tooling has to be changed for not more than 3 cases, so manufacturing cost of high. But also because it is used in higher purities and requires more effort to work into a final shape. So as traditional practice in marking prices of watch, Platinum is used to be the Most expensive line of the Watch, then Pink gold, White Gold, yellow gold.
Take Rolex watch Price as for examples, make it a stainless steel as 1. the Two one is about 1.7X Yellow gold is 4X, Rose Gold is 5X, Platinum is 7X.
Other case materials which one will run across occasionally (especially on the vintage market) are Sterling Silver (92.5% purity silver), Coin silver (80% purity silver), nickel silver or silveroid (not silver, but 66% copper, 24% zinc, and 10% nickel), nickel, and nickel plated steel. Also, more recently, one can even find watch cases made of ceramic (zirconium oxide, Rado has been using for many years as used recently by IWC) and aluminum (used in conjunction with other metals, as currently used by Porsche Design and BVLGARI.)
Titanium is a relatively light-weight metal, with a hardness exceeding that of most steels. It also has a poor heat conductivity character, which means that it won't carry heat away from your skin as quickly as steel or aluminum (i.e. it will feel warmer to the touch - sometimes you'll see claims that titanium "remains at skin temperature" - this is technically incorrect, any more than a small piece of wood stays at skin temperature). Several varieties of titanium are available. Titanium has some interesting mechanical properties: it can "rip" when cut so it is difficult to machine, and two pieces of titanium pressed together can "weld" themselves together.
This latter property is why it is important that watches with titanium cases and backs have the casebacks removed periodically - the threads can actually rip out of the case if left undisturbed too long.
Later trend like AP introduces the carbon Fibre that has to be molded under hi temperature and pressure.
Rado has been using unscratchable ceramic material to make watch for many years..
Plastic watch case has vibrant colour that has no limit at all, but the sweat that goes into the plastic will ultimately changes colour of the plastic, the plastic will become brittle after years. It may crack. So only cheap watch use plastic to make cases.
So what is the best material to make watch cases, my opinion is Platinum as it is precious metal that has a dull silver grey colour. Rose gold because of the colour is beautiful and classical look. White gold as it is like stainless steel, good low profile metal for cases, yellow gold that shines the way forever when you wear it on your write. Titanium is good for sport watch as it seem has it unique colour and super light weight yet strong to resist scratches, Ceramic is not a good material a sit is too cold on my hand. Plastic is limited to be used for low cost watch I believe, though there has been a trend for expensive watch case to have some plastic parts on the watch cases Like AP. But I don't like it at all.
Attached picture is a Rolex Oyster watch case made of solid single piece of 18KT Yellow Gold.