Yes, tri suits are fine to wear for the duration of a triathlon. They're usually a bit more expensive than a pair of tri shorts and a tri singlet/top, but tri suits are often more aerodynamic than a two-piece outfit, and you can dump ice down your suit on a long day without worrying about the ice excaping through the bottom of your jersey. Plus they make my spare tire look smaller!
Also, some of the top-of-the-line tri suits (speedsuits) have hydrodynamic properties (making you faster in the swim), and have ITU-legal back zippers.
As far as a good brand, it really depends on what fits you. I have found that DeSoto trisuits run a bit small in the shorts portion, Zoot runs a bit large in the top portion, and Voler fits me just right
But, if you can get to a physical store and try a bunch on, that's really your best option.