Most types of stainless steel are not fully rust proof. For a good compromise between high effectiveness rust resistance and cost, look for products made of 316 stainless steel. This type of steel is unlikely to ever rust. 304 is also pretty good.
For brewing devices, a percolator, a moka pot, or a French press could all do you right. All three of these choices are available on all-metal designs including aluminum and stainless steel.
I recommend the French press form simplicity. Simply place grinds and hot water in together, let brew, press, and pour. Doesn't get easier than that.
Moka pots and percolators are nice gadgets that produce lovely coffee brews. They're both more involved to use and more work to clean than a press. Still, they make great coffee.
So yeah. Recommend one of these three devices with 316 or 304 stainless. Pour over gadgets are often available in glass, too, but these will require paper or stainless steel filters.
Alternatively, you might consider trying cold brew in a glass pitcher or jar.