Screws are probably better for people without a lot of wood working experience. They pull the wood together and form a tighter, stronger bond.
Nails are also just fine though. If you come from a long line of professional carpenter's and have picked up a couple tips in your life and know what you are doing, there's nothing wrong with using nails. They are more asthetically pleasing, they are less likely to split the wood, and easier to work with.
However, the glue is what should be doing a good majority of the holding. The nails/screws should only act as a reinforcement. That's why you shouldn't go cheap on glue and get the $5 bundle pack of 6 bottles of Bubba's Special from Sam's. Go to a real hardware store and get something like Gorrila Glue or Titebond.
But more importantly, it depends on what you are building. If you're going to build a massive 10 cubic foot box, I would naturally use screws all the way around, along with supportive bracing. If you're going to make a medium sized box, I would use screws in a couple important spots, like on the bracing itself, and nails the rest of the way. Then for a much smaller box, like the one in my sig, I only used a nail gun and glue with no bracing.
As for clamps, they are important. People use them for a reason. Unless you want you shit falling apart, I would use them. Just don't go overboard. The purpose of a clamp is to hold multiple pieces of material together and stable till the glue dries and bonds. Not to clamp it so tightly that all the glue gets squeezed out of the joint.