Best war trait is Charismatic by a mile. Expansive and Aggressive are also helpful for early attacks, with an economic tech being a better pairing for later warring. Financial helps pay for expenses through more commerce for income. Organized cheapens the cost of those cities you take and you can further reduce it by whipping angry faces away into a courthouse as soon as any 4+ pop city comes online. SPI civs deserve a special mention because they can flip into war civics at a moment's notice or toggle between a couple civics constantly to benefit from both as needed.
-When rushes came to mind, the first one I thought of was Qin Shi Huang. Cho-ko-nu rush is crazy and he's backed up by the IND trait.
-UU + traits says Cyrus. Immortal is good for rushes while CHA+IMP means super promoted units in the long run with all those GGs and cheaper XP costs.
-UB+ traits Shaka is awesome and my favorite for early rushing Axes or Swords. Slap down a granary and Ikhanda while securing your metal and looking around with your scout. Impi make awesome choke units and serve well cutting off resources because of Mobility. Shaka is crutched by having to make his early game advantage work for him though, by capturing cities/getting land or eliminating close opponents.
-Boudica has the best trait combo for early war but crappy UU, UB and techs slow her down a lot for anything early, which wastes her AGG trait. Melee units also disappear after Maces, meaning she doesn't even get a good window to use it at all really. Brennus is not really any better, with the same problems, but SPI is better than AGG for anything past the early game.
-Washington is surprisingly good for early attacks because of his trait combo of EXP/CHA. EXP speeds up rushes by cranking that granary for whips and workers for chops faster, and CHA helps you whip more leniently. The other two, not so much, even though Lincoln is CHA, there is no UU or UB help and PHI isn't exactly a war tech unless you do some tricky stuff with Great Merchants+upgrading after CoL.
-Tokugawa is utterly gimped getting to the gunpowder stage of the game, but if he gets there his Rifles are insane, almost like a UU themselves and way better than the Samurai. He also can handle warfare earlier pretty well, with AGG for offense and PRO for when you have to fall back and weather an assault.
-Churchill is similar to Toku, but with a good UU to go along with the traits that pump it up. He lacks the early game punch of AGG, but makes up for it later.
-Gandhi can pull off macro-oriented upgrade-based rush attacks at the drop of a hat. Get CoL (Oracle might be a nice way), run merchants, build a bunch of warriors while collected some Great Merchant. When you're ready to attack, cash in and upgrade, flip your civics to war focus for your reinforcements and power through the enemy with a wave of suddenly upgraded axes/maces. Any PHI can potentially do this but Gandhi never need worry about anarchy when swapping in and out of war mode at any time. I actually think Lincoln might be better at this in terms of unit promoting, but Gandhi's UU, UB (which helps in later war) and no anarchy ever put him ahead
-Obligatory Romans response. AC better for later, JC for earlier. Praetorians are nothing to sneeze at if beelined.
-I have used Glgamesh well in early wars. The Vulture UU trashes Archers with CR upgrades, can deal with horses, swords and catapults, even other axes well, and his Ziggurat helps with the expenses of conquering cities.
-Spanish can be crazy in the mid game all the way to modern. Powerful Cuir UU that gets defensive bonuses and eats pikemen, when Cuirs are already great, UB makes for some monster Trebs and Cannons if you want to go the slow and steady route. Suffers in the early game though, and she has no economic help.
-Hannibal has an okay UU rush and great overall trait combo for being good at both econ and war. Even without a successful Numidian rush, his FIN economy and CHA units make him a good general warfarer.