Not a cosim, but if you want to spend good time with 2 or 3 friends (4 or 5 with material expansions), try "Settlers of Catan", which has proven to attract both younger and older generations alike, and is both rivalry and communication, mild strategy and cooperation (or not
). It's the most successful game from German production of the past 20 years or so. I recommend to use the basic game together with the Städte&Ritter (knights and cities) expansion.
For pure strategy, obviously nothing beats Chess, or if you prefer: Go. If exclusive thought duels are your thing, give Abalone a try, too - simple but elegant in rule design, fascinatinjg and again elegant in challenge and diversity.
I have started threats in the past, one on Abalaone, and one on Catan. Use the search-button for more details and feedback, also computer-versions (of both games that can be tried for free. That would give you an insight into the game mechanisms.
From the pre-PC era, cosims I knew and would recommend if you can get them second hand are Game Desiogner'S Workshop's "Third World War" series (probably my most favourite cosim ever, covering the war from Scandinavia over Germany and the Balkans down to the Gulf and Iran; also nice solitary play, btw), Victory Game's "Gulf Strike" and "Aegean Strike" (not really for beginners), "2nd Fleet" and "6th Fleet" (good introduction to the naval genre, not too complex), and GDW's "Assault!" series. I also owned Avalaon Hill's "Flight Leader" and "Ambush!", a dedicated exclusive soloplay title with - for it'S time - an innovative soloplay mode. Subsim mainpage also holds my feature of that old naval game "Tokyo Express", to be found under "Reviews". It is dedicated soloplay , with a nicely functioning "AI" to control the enemy fleet's movements, and has expansion rules for 2-player game. Complexity can range from beginner's level to quite advanced levels, via optional rules.