Too many variables. For example what do you mean by a war game. Do you mean you fight when attacked. Does it mean once a war starts you never make peace.
What is a peace game, no wars, no starting war, make peace as soon as it is offered?
At what point in the game do you want these wars?
I would not expect the Mongols to be a common pick for war games. I could see Rome for early wars, France for any time/era. China for Middle Age is not bad.
I like France for nealry any type as they are Commercial, get a jump on the Writing path. Great UU as it is not too early. Their traits allow you to build many wonders and not trigger a GA. You can avoid a GA from the UU with no problem.
If the map is pan or continents these are fine, if it is an island map you may want to change. I think there is an article on all the nation in the Strat article forum. Not studied it, so not sure how good it is, but someone at least gave some thought to them.