If you want a more up-to-date, refined, and traditional TW game, Total War: Shogun 2 is very, very cool albeit on a less grand scale than other titles in the genre. If you've never played before, I'd start the original game or Rise of the Samurai first, then play Fall of the Samurai. Personally, my favorite is Fall of the Samurai but the emphasis on more modern artillery and firearms departs significantly from the gameplay of the signature titles, which I would consider to be Total War: Rome or Total War: Medieval 2. Rome was cool because of the vast variety in units and factions, somewhat similar with Medieval. Shogun 2 is just better overall as far as the base game goes for graphics and AI IMO, if you're looking for something from this decade and something to really take advantage of your hardware.
The one pitfall I see in Shogun 2 is that it lacks quite a bit in unit variety as opposed to Rome and Medieval. It's pretty much Imperial vs. Shogunate and largely the units for each side mirror each other, with most of the units available to both sides, and the mid/late game end up with massive armies of largely the same units (rifle infantry/spearmen/spear cavalry/artillery cannons/rifle cavalry). There's a few cool mods that can change it up a bit and alter strategy, such as DarthMod, which makes cavalry of all types much, much more formidable against rifle/bow infantry, but doesn't add much in unit variety.
Also, the ship battles in Shogun 2 are fucking awesome, with iron hulled ships pummeling each other with armor piercing cannons and catching the odd wooden ship with explosive rounds for a very big explosion.