Being militaristic is a great Civilization trait, and the Romans are an excellent Civilization in the game. Being militaristic means more of a chance of upgrading as a result of combat, this means more veteran and elite units; more elite units means more great leader opportunities.
Further, barracks are alot cheaper. So cheap in fact, that early cities can build a barracks in between building settlers. Non-militaristic civilizations have to forego building of settlers, and thus expansion opportunities, early on if they want to build barracks - militaristic civilizations don't; this is a pretty substantial advantage - early on militaristic civs have veteran units, non-militaristic civs don't.
An added, but not-to-be-underrated bonus that militaristic civilizations get are cheap harbours. Harbours are a valuable improvement, but they are very expensive for a fledgling civilization to devote resources to building early in the game. The reduced cost helps alot, giving militaristic civilizations a naval advantage early on. Also remember, if you want to found a colony-city over the seas, next to some resource, you need a harbour to ship the goods back home. For a colony-city to build a harbour is exorbitant, but so much easier for militaristic civilizations.
Also, commercial isn't to be underrated imho. People expect the corruption to be far far lower - it's not. But it is a little lower, sometimes turning 1 shield into 2; which can make a large difference. Further, the extra commerce is nice, especially early on. It allows you to get that bit of extra gold or research that little bit faster. Remember, when you build your first city, you might get 1-2 commerce. With a commercial civilization you get 2-3.
Also, legions are a very nice, solid unit. They are excellent on attack, particularly because your enemy simply has no counter-attacking opportunities. Sure, they don't quite have the city-taking brilliance of the immortals, but enemies simply can't fight back. You can march legions up to enemy cities, plant them outside, wait until you have enough then attack. With immortals, enemies can counterattack with archers very economically (an archer attacking has a 50/50 chance of killing an immortal, and is cheaper), or with horsemen (if the horsemen are losing they can retreat and thus are very economical for attacking immortals). With legions, attempting any counter-attack with less than swordsmen and catapults seems rather futile.
Also consider the stats of a legion facing an immortal head-to-head. On an open field if the legion attacks it has a 3/5 (60%) chance of winning each round; an immortal has 4/7 (57%). A narrow advantage for the legion.