Aluminum, copper, and stainless steel all work fine for brewing. Each has advantages and disadvantages. Before buying a kettle, determine budget, capacity needed, how often it will be used, and how long it is expected to last.
Aluminum: Often comes in either brushed or polished. This is just appearance. May be thick or thin. Transfers heat very well. Low quality aluminum is thin and may not last many years. Lighter than stainless steel. Do not use a kettle that was used for cooking food. Acids may have soaked into metal and can affect beer.
Stainless steel: More expensive than aluminum, but if taken care of, it will last a lifetime. Thick steel can withstand more use and will not bend as easily as thin steel. Heat transfer is not as good as aluminum. Some have a copper base or an aluminum core which transfers heat better. Low quality stainless steel may bend, oxidize, stain, or corrode. Heavier than aluminum.
Copper: Expensive. Conducts heat better than stainless steel. Not cost effective. Only recommended for those who already own copper kettles or find some at a good price. Copper will not work on induction stoves. For these reasons, it is not discussed again.
Enamel coated steel: Commonly dark blue, sometimes gray. These are steel kettles which have been coated with a protective layer to prevent rust. Often very inexpensive. Will work fine as a brewing kettle as long as the enamel is not chipped. Once chipped, the steel will rust and should not be used.
Cheap kettles are usually made from thin, low quality metal. They will work, but cheap stainless steel may rust, bend easily, and both stainless steel and aluminum may not last for many years. It is best to make a larger investment and buy a good quality kettle.
There is no absolute best metal to use. Which to buy will depend on budget and needs. Good quality aluminum kettles will work just as good as stainless steel.
Less expensive than stainless steel
Much better at conducting heat, boils and cools faster
Easy to drill
Oxidizes easily, so caustic and oxygen based cleaners should not be used (avoid Oxyclean, One Step)
Passive oxide layer must be made before initial use
Do not use abrasive cleaners or metal scratch pads
Softer than steel, easier to dent, but can be pounded back into shape with a rubber mallet
Stronger than aluminum
Any cleaner can be used
Already has passive oxide layer
High quality will last a lifetime if properly maintained
Thick, good quality steel is heavy
Not as good as aluminum at conducting heat
Hard to drill