Kab:
Bill covered the basics admirably, so I'll just throw in a few extras.
There's absolutely nothing wrong with hand-brushing your models. We all started there, and many folks still do it and get excellent results. In general, however, it's easier to get a clean finish with an airbrush--the only dial-in you really need to deal with is the thickness of your paint mix, no need to worry about brush strokes and such.
A major problem with hand-brushing is that certain types/brands of paint don't really lend themselves to hand-brushing very well. Chief among these may be Tamiya acrylics; though I like them, and use them almost exclusively, I'll be the first to admit that hand-brushing them over large areas is tough, since they're so fast-setting (even with retarder added) that the newly-applied brush strokes seem to grab and raise the adjacent laid-down areas with distressing regularity.
Having said that, they're excellent and virtually trouble-free for airbrushing. Easy to apply, easy to clean up, and they give a durable and easy-to-mask surface. Depending on how technical your approach is, they do have the drawback of a somewhat limited color range for some of the colors that military modelers use regularly, but I'm an advocate of paint-mixing so that's usually not a problem.
Last, as a dedicated four-piper fan, which USS Ward are you doing? You used it as your title, but didn't actually mention the kit.
Regards