You say you like war and conspiracy, huh? Fullmetal Alchemist or almost anything with Gundam in the title would suit you well.
I keep a rotation of about four different anime series that I watch at a time: two super long runners that never seem to end, like Naruto and Bleach (DBZ, InuYasha, and One Piece are also good for this). These kinds of shows don't take a lot of brain power and allow you to either watch sparingly and come back, yet pick up quickly on the plot, or to go on a binge and watch a dozen episodes a day, if that's your thing.
I also watch two series that have a designated beginning, middle and end based on the 13/26 episode season format, like Ghost in the Shell, Blood+ and Death Note. These kind of shows are usually better in terms of plot and character development, because they contain far less filler and waste less time getting to the point.
Hulu is a great place to find lots of free anime. PLEASE support legal+free anime!