How warry do you want it to be?
I still love Onitama, which is quick and light and done in ten minutes, twenty at most. It’s a wargame in much the same way that Chess is a wargame, i.e. not very.
Or there’s Memoir '44 (SU&SD have done a review and a Let’s Play, and I ran a PBF game here), which is one of the many implementations of the Command and Colours metasystem – it’s not very flavourful in terms of the specific characteristics of a particular conflict but it’s definitely a wargame.
Then there are lots of “troops on a map” games – not so much my sort of thing but Blood Rage gets mentioned a lot. Some of these spread out from direct military action to allow conquest by other means too.
It sounds as though you’re after a “wargame in a box” experience rather than lots of collecting and assembling (and painting) armies over an extended period, but you might look over in the miniatures thread for more on that. Some of the miniatures-based games have relatively low barriers to entry.