The best thing about the Redcoat is that it appears for free when the English found cities on other continents (after Military Science is researched, of course). This means additional defense for these cities right from the start, not to mention the free unit. And, as with all civilization-specific units, the Redcoat requires no strategic resources, which is a great boon during a game in which the player has been unable to secure Niter for Musketmen, and his or her melee infantry is stuck in the Classical Era. Unfortunately, they won't be able to upgrade to Redcoats.
A great tactic for these troops is to mass them until you're ready to launch an offensive. Since you receive a Redcoat every time you found/conquer a city on a different continent, you will be constantly gaining more and more military strength that you can turn against your opponents. Bear in mind, however, that Redcoats are quite expensive to maintain, so if you conquer too many cities you won't be able to afford the Redcoats and may go bankrupt. If you plan on making a Redcoat army, you must make sure your economy can handle it.
Historical Context Edit
The red (or, more accurately, the shade rose madder) coat of the British infantry evolved from the ceremonial uniforms of the early 1600s; it was officially adopted in February 1645 AD when Parliament drafted the regulations for the New Model Army, with the 12 regiments of foot all wearing red coats with different colored facings to distinguish between them. For the next quarter-millennia most of the British infantry wore such, making them splendid targets among the trees, dunes, jungles and hills of the Empire. The rationale for such a choice was that (despite the fiction it was because bloodstains were disheartening for the men) red coats were instantly identifiable on the field in an age prior to use of smokeless powder, where battlefield visibility was a greater problem than tactical concealment. This choice of uniform hence helped maintain order, combat efficiency and morale (although not all British forces would use red uniforms). The term “redcoat” became a source of pride for the British, and a curse word for just about everyone else.