And why not "a full suit of armor"? It works pretty well for the movie Batman. And while sure, characters like Conan or Red Sonja can get away with little to no armor because they rely on their skill with steel to protect them from enemy weapons, they don't exist in a world with guns. Skill doesn't trump bullets. And no matter how good one is, it only takes one lucky shot to an unprotected body to be the end of anyone. Body armor is a necessity for survival, plain and simple.
Of course, that doesn't mean everyone suddenly becomes Iron Man --though I've long thought something like Batman's Kingdom Come armor would be awesome for him, just don't overpower it. That aside, there is a reason not to load everyone up with full plate. Body armor is always a trade-off, protection for encumberance. The tougher the armor, the heavier and more restrictive it is. Thus, a character like Catwoman wouldn't wear anything thicker than she has to, relying more on her stealth and agility and wearing just enough to stop an average round in case she gets tagged despite her best efforts. She'll never walk through gunfire and shrug it off, she'll never wear that much protection as it would slow her down too much. It's detrimental to her combat style to wear too much armor.
It helps, fortunately, that comic book materials are available to make that balance a little easier to strike. For example, in Marvel SHIELD agent uniforms and some variants of the X-Men standard issue suits are made of materials that are no bulkier than the average spandex bodysuit and yet provide protection equivalent to modern kevlar. It's not unlikely at all to say that similar technology is available in the DCU, meaning you don't have to bulk a character up to protect them. That said, however, no material no matter how advanced is going to protect areas of the body it doesn't cover. So plunging V-necks and belly dancer navel windows and exposed thighs (femoral arteries are bad news when severed) are a bad idea for any character who relies on their costume to protect them.