This is relevant to my interests.
I would also speak in favor of not necessarily making every game a military/conquer focus- if the premise is time traveling agencies, after all, then even business sims might decide the future of the world. Imagine if somebody came back from the future and gave Apple the edge over Microsoft, or built such an awesome zoo in Berlin in the 30's that Hitler decided to become a naturalist. Although obviously, strategy/FPS's are awesome and worth including on their own merits anyway. Sometimes direct solutions are the best, after all.
Looking through my personal games library, I'm reminded of how little money I've had to spend on them the last few years. Notable games currently on my hard drive include (but are not limited to) Minecraft, DF (obviously,) Kerbal Space Program, Nethack (maybe as some odd virtual cyberpunk world?) Quake I-III and Civ IV (plus expansions.) A glance in my games cabinet reveals Rome: Total War, Medieval II: Total War, Age of Empires II, Age of Mythology (plus expansion,) Sins of a Solar Empire (plus expansions) and Galactic Civilizations II.
I also think Flash games have merit, what with being readily available to anyone, as well as the fact that score systems lend themselves to indirect competition. The big thing there is finding the 10% of Flash games that don't suck. Browsing my favorites on Kongregate yields Fly or Die Multiplayer (strategic turn based dogfighting,) Second Person Shooter Zeta (as opposed to First/Third Person shooters, it's pretty trippy,) World Rebellion II (Risk clone, some extra maps,) Crunchball 3000, and Red (kinda like Nimbus Commander with bouncy balls on Mars) as candidates that don't suck and might be workable into missions.
In any event, count me in!