Which type of frame is better for a touring bike, steel or aluminium? I hear that a steel frame is more comfortable to ride for a long tour but that it is heavier and easier to rust than aluminum.
Which material is better for a touring frame?
Steel is still very common for relatively expensive "touring" bikes (bikes intended for long distances carrying panniers).  The slight additional weight of a steel frame over aluminum (well less than 10 pounds in most cases) is inconsequential when you have 40-100 pounds of gear on the bike, the bike is more durable, and the flexibility of a steel bike is preferred by many on a long ride.

Aluminum is more rigid because the tubes must be made fatter and thicker to achieve the same yield strength as steel.  In some contexts this additional stiffness may be appreciated, but generally not when riding long distances.

Stainless is hardly ever (never?) used for bikes because it's too hard to work with and the metallurgy doesn't allow the characteristics of the material to be  controlled nearly as well as steel or aluminum.  And its heavy.

Carbon fiber is carbon fiber.  Great for lightweight frames (saves another 2-5 pounds, maybe), great for bragging rights, but fragile and often excessively rigid.

One important consideration on a cross-country ride is that a steel frame is very unlikely to suffer fatigue failure, while the other materials are considerably more likely to do this.  (And, in a pinch, a steel frame can be repaired by a welder at a local auto or tractor shop, while a broken aluminum or carbon frame is likely toast.)  (Of course, any good quality frame that isn't overloaded should hold up to a 3000 mile journey, but sometimes things happen.)

The tendency of a steel bike to rust is of little consequence.  A steel bike would need to be exposed to the weather constantly for 20 years before rust would cause a failure, and at that point all of the components would have already disintegrated.  And I don't know about carbon, but aluminum and stainless steel tend to suffer crystallization of the metal at the welds as they corrode, and this can lead to sudden joint failure.