I play Xbox, and only local multiplayer games. (As opposed to online. I play against people in the same room.)
Assuming that the fanboys are right, and the extensive PS2 catalog has all the Xbox stuff plus a billion more, I’m just going to list the Xbox games I play and figure PS2 has them as well.
Top Spin: It’s the greatest tennis game since pong. Very fun, extremely simple and straightforward control scheme, and you have your choice of head to head or gang up doubles style against two comps. (Or head to head doubles with one comp player per side.) This game rocks, and is exactly your speed. Trust me.
X-Men Legends: Or whatever it’s called. Very fun. Minimal inventory maintenance, where you only equip maybe 3 total items per person, and each character has maybe 6 mutant powers to level up. Simple button controls, no dexterity required. It’s perfectly suited for both you and a 13 year old.
Madden: The grandaddy of all games. Might be a bit involved, but if you both get into it, and each take a different team in a franchise, managing and playing your teams through multiple seasons is probably the most satisfying gaming experience there is to be had. If you do the two team franchise route, be sure your either a) both in the same division, or b) in different conferences. A third option would be to play as a single team (one calls plays and passes and the other runs and catches) against the computer in franchise mode, but playing against the computer is boring and pointless, IMO.
NBA Live: IMO, EA’s game (Live) is better than ESPN’s, but opinions vary wildly. We like Live because you earn dynasty points for doing good things (like a triple double, etc…) and can then spend those points either developing players in permanent training or buying temporary coaches to boost the entire team. Basketball in general is not nearly as satisfying in regards to multi-season franchise development, but the dynasty extras in Live make up for that. Plus, it’s the ultimate team game. One guy controls the perimeter (pass and shoot) while the other handles the baseline (blocks and rebounds.) Probably our current favorite for satisfying gameplay. Works equally well as a 2-player, 3-player, and 4-player game.
I get together with three other guys once a week and play Xbox games. While we also occasionally play Halo online, the above games are what we spend 99% of our time doing.
Personally, I think the best bet if you can get into it is Madden franchise mode. It draws you in with the managing of the rosters (drafts, trades, free agents, retiring players, player development through production / winning) which lends itself to strategic planning and conversations outside of playing. In other words, of all the games I mentioned, only a Madden franchise would come up in a random breakfast coversation between you and your son. Why would you talk about Tennis or X-Men? You wouldn’t. But you might find yourself talking about a Madden franchise a fair amount. (“So have you figured out what you wanna do about your injured starting running back yet? The trading deadline is next week, but remember you’re up against the salary cap, so you’ll likely have to put him on injured reserve to free up cap space.”) IMO, sports in general (and Madden) can be a wonderful conversation lubricant between a father and his teenage son.
We’re old guys, so what we find works best is to play once a week as I said, (most of us don’t even turn our Xbox on during the week) and play as follows:
1 week of Madden (4 games, or fewer if someone has a bye or head to head game)
1 NBA Live Game (10 minute quarters, allowing easy quadruple doubles)
1 TopSpin doubles match (5 sets, 6 games per set, like actual tennis)
1 checkpoint in X-Men, or at least a half hour
That’s a good solid night, is quite fun, not repetitive, and all the games are fairly easy to control without needing much dexterity. I highly recommend it.