You have your mask (if any) you have your cape (if any, I don't judge.) Both are optional but the rest of the costume kind of ties things together and keeps you from being socked with indecent exposure charges (I want to see the cop with the balls to ticket Dr. Manhattan though.) There are several costume genres.
Realistic, also known as cheap, means you're buying stuff off the rack or maybe fighting crime in normal clothing. Normal clothing has a tremendous advantage for the secret identity user. No one can go through your closet and discover your union suit thus outing you (That thing? I wore it to Mardi Gras. Yeah I know it's bulletproof and flame retardant; have you ever been to New Orleans?!)
As an alternative to street clothes a hero could wear athletic gear (enter ... the Quarterback!) Some rigs, particularly for dirt bike riders looks made for supers. They also can afford some protection (speaking of which an athletic cup could pay for itself many times over even if you wear street clothes.) A little dye job or repainting and you're ready to go.
Some supers incorporate armor into their uniforms. This can be seamlessly tailored in or a general issue BP vest. Realistically it is doubtful a skintight outfit could incorporate protection against anything larger than pistol rounds with current technology. I''m going to buck the current trade of RPGs in general and go with the SCA people when I say armor doesn't necessarily impede you. Even the Middle Ages, knightsy stuff let the wearer climb ladders, perform shoulder rolls and, in the case of chainmail at least, swim! However armor does tire the wearer out and make them more prone to overheating which can be a large factor when you're patrolling on foot.
Speaking of overheating there is a practical reason for skimpy costumes (other than sales.) People running around and socking people all night get hot. You want some exposed skin to cool off quickly. The Green Hornet must have had the endurance of Hercules fighting crime in a business suit and trench coat. Batman never seems to have a problem with this but hey, when did you ever see him sweat?
The four color conventions say a hero's costume is immune to their (usual) activities. In other words Matchstick Girl doesn't burn her costume up and become Fan Service Girl every time she combusts. Your average brick can get slugged through a razor blade factory without seriously damaging their clothes. explanations for this effect run from handy side effects (I generate a skintight forcefield that protects my costume), to pseudo science (unbelievable molecules mimic our power effects and aren't damaged by them) to hard science (Beta Cloth is used by NASA and can withstand a temperature of 2760 degrees C. go look it up) to practical (This isn't a silk screened orange shirt, it's orichalcum mail, a symbol of Atlantean royalty!)
Even super powered characters might want to consider costumes that afford some protection. Sure you're invulnerable now but one day your nemesis might wise up and carry a handgun along with his power nullifier ray. For that matter you wonder how much easier Superman's life would be if he just incorporated a layer of lead foil in his uniform. If your super needs frequent contact with some substance to maintain his powers or health he could include some of that in his outfit. It makes you wonder why Dracula never carried some native soil on him. If Van Helsing finds your coffin, just sprinkle a little dirt in any old crate for the day. In one series Aquaman wore a version of his costume that stored sea water allowing him to spend more time on dry land.
As a final bit of compulsiveness keep in mind your super doesn't have to have one costume. He could have different versions for summer or winter or with modified armor when he knows he's going up against heavy firepower for example. Besides, would you wear the same civilian clothes everyday?