well.
the word polygon means "many sided shape". so, you could be building with 6 sided faces, and they would still be polygons. so counting polygons isnt really accurate.
you count triangles, because when the model goes in-game, it will be trianglulated, and thats how the engine reads it.
a good triangle count is kinda a tricky thing... its basically about how detailed the model is. personally i think anything over 3000 is a waste. especially if there is little detail. you should always aim for the lowest count you possibly can, while keeping the most important thing in mind, which is usually, how well itll animate.
always make each vertex define something, if its not defining anything, then it doesnt need to be there, and your just using a wasted poly when it could be used better somewhere else.
look at it this way. the more triangles, the more the gpu needs to process. you might think "the engine can handle it". and sure, hl2 can handle 4000+ (just an example). but if its going into multiplayer. peoples cards might struggle to render 20 players with high poly models.