Tabletop is pretty entertaining show that gives you the general rules and strategy of each game while being filled with nerds and dick jokes.

I've quickly become the owner of a pile of the euro-style boardgames.

If I had to recommend one game I would suggest Pandemic. It's great. Totally cooperative where you work with your fellow players against the outbreak of several viruses. It's hard as hell, but very fun.

If you have parties with lots of people, Avalon (or Resistance) is a live Werewolf-type game that is lots of fun but requires 6+ people to play.

I could list loads of other games but these are two very different games that give you a good place to start.