World in Flames. Check out the AAR's. As for your basic principles:
1. Randomization. (very high), although this game has no AI and is meant to be played vs human opponents.
2. Replay value. (extremely high, actually unlimited). You will spend the rest of your life intrigued by it.
3. Historical accuracy. (very low). While there are actual units that participated...especially every naval vessel from cruisers and up represented from every major and minor nation and air units, there are some late war fantasy units as well. There is no historical set up, everything comes down to your own placements and purchases. In a way, it would help to be a fantasist.
4. Time period. Fits.
You might want to consider two more basic principles: Game Support. Is the game currently being supported by either the original developer (updates, bugs, etc...), or by dedicated fans such as Steel Panthers (another good pick)? The other principle is: Universe of players playing the game. WiF is huge and has conventions around the world.
+1 Best Game Ever - (but please note this game still has issues which anyone on that forum would be happy to discuss if you are interested)
I would add something to Historical Accuracy though.
The game is designed to be one that can be won by either side. For that reason there are liberties taken for game balance purposes with some of the unit factors (and no doubt the unit numbers). That said however, the game does provide players with an historical framework to ensure that each game has a proper WWII feel e.g. The Axis are the Axis - Italy, Germany and Japan and the Allies are the Allies, CW, France, China and, ultimately the USA and the USSR (there is a clever US entry system and a Nazi-Soviet pact to keep things in check). Within that framework players can do pretty much what they want (with some exceptions) although in WIF, every action in the early part of the war by both sides has a potential effect on all important US Entry - so its never a free for all.
If you want a fun - but very difficult to master - game that encompasses the entire war, and is set out on a beautiful map of the whole world!, with NATO counters for the armies, and full colour silhouettes of the ships and aircraft that took part in WWII then look no further.
England expects that every man will do his duty. Horatio Nelson October 1805