Pandemic is a good, relatively simple cooperative game. Also pretty cheap.
Beyond that, it would help to know a bit of your interests. I mentioned Eldritch Horror above - it's a more complex cooperative game with a horror theme. Basically, you're traveling round the world trying to prevent it from being destroyed or devoured by one of various horrible monstronsities, or before your characters die or go insane. Mansions of Madness basically involves creeping around a house, trying to find clues and other things before some something horrible happens...or again, going insane or being killed. Second Edition is great because an app makes setup much easier.
If you want a true wargame, then knowing the period/themes in which you are interested would help. There are historical games from World War 2, Napoleonic, ancient, etc. etc., then there are some games based on Lord of the Rings, Star Wars, etc...