hoi3 was developed under vista. vista uses the same kernel as 7 so it is nonsense to run the game in compatibility mode.
thank god I am now developing HoI3 under Win 7 instead, so you shouldnt have to worry about that.
the UAC is horribly terribly bad if you are used to OSX security but you learn to live with it.
get 64-bit version for future proofness. as for ram as a regular user not doing anythign too wacky 4GB is fine. when I do video editing or run multiple development studios/debug modes of games it starts approaching 4GB tho so I have 6.
also if you are considering a whole new computer and have some money a solid state drive for at least windows and your most used programs is fantastic for startup and load speeds.