If you like big battles, explosions, and the ability to Command an Army Navy and Airforce get Total Annihilation or Supreme Commander 1 or 2. I recommend 2 for something casual, 1 for something extreme and more variety. Total Annihilation is great because of its simple 2d graphics, amazing soundtrack, and more interesting story also you can get it for five bucks.
If you want something more fast paced with combat dictated with ques and combinations, or has an interesting story and some dark humor get Starcraft 2. This game is kind of pricy. Not so much Strategy here, but rather thinking about what beats what. Kind of like rock paper sisscors.
For a somewhat casual take over the world or whatever type of game get Civilization 4 or 5. The game has a somewhat a learning curve, and its kind of pricy.
If you want to get really hardcore grand strategy game similar to Civilization and start slow at the start of the game and what the action pick up fast I recommend any of the Paradox games. You have Europa 3, Hearts of Iron 3(this one is my favorite, dlcs are recommened), and Victoria 2. Best part these games are cheap and good. So in Europa 3 starts you from the End of the Viking Age and takes you all the way to the Fall of Napolean, so you can play as any country in the world as well as several native american tribes. You are dealing with trade, war, governing your people, and researching new technology and colonizing the Americas. Victoria 2 takes place during the Industrial and ends ten years after World War 1, in Victoria 2 you are mostly deeling with the politics of your country, colonising Africa, and sometimes going to war. Hearts of Iron 3 is a World War 2 game which is similar to Europa and Victoria, but the gameplay focuses on Warfare itself. In Hearts of Iron 3 you will be building small brigades to corps to large armies. Like the other games mentioned you can Play as the USA and join the Axis powers if you wanted to. These games are slow and require alot of thinking. I suggest watching youtube videos on these before buying. Also consider Arsenal of Democracy as an Alternative to Hearts Of Iron 3.
If you do get Victoria 2, Hearts of Iron3 or Europa 3 I can teach you how to play, but if you want action and cgi with thinking thrown in I would consider getting Supreme Commander.
