For miniature wargaming (moving figurines around a table, as opposed to a board game), check out DBA: https://www.amazon.com/Laflin-Barkers-Start-Ancient-Wargamin...

The rules are pretty elegant and fun, and are quick to teach and play. A game usually runs 30 minutes to an hour. Miniature wargaming is always going to be a bigger investment in money and effort than a board game, but DBA is pretty easy to get into: you only need a couple dozen figurines for an army, and a playing surface of about two or three feet square.

The central conceit of the rules is that the important thing is modeling a unit's role on the battlefield, and the rest can be abstracted away. So for example a unit of pikemen is a unit of pikemen, whether they're a Macedonian phalanx or a Swiss landsknecht. This lets the same set of rules support battles from the bronze age to the renaissance.