Many gamers ponder where to go after the into/gateway games. They like the ideas put forth in those types of games, but they want something a little deeper, a little longer, maybe a little bit more complicated. Many factors come in to play here, but the key question is what have they played. Here are some of the games I've had success with when it comes to furthering someone's interest/love in games.
Acquire is a classic from noted designer Sid Sackson. Players place tiles on the board to increase the size of hotels. They then buy stock in hotel chains on the board. The goal is to merge hotels, have your hotel taken over so you get paid out on stock, and then to invest in large hotels for the end of the game. It's not the most intuitive game at first, but it is a familiar concept for many adults due to the stock nature of the game. It takes about 90 minutes to play, and it makes you think, but I enjoy it from time to time.
Cosmic is the second designer game that I ever played, so it has a soft spot in my heart. Getting into the game can take time due to a variety of card effects, but this is less for all new players. Cosmic focuses on hand management and negotiation. It is a confrontational game, but rarely is it a "beat-up on one person" game. Cosmic has a great deal of variety, with 50 unique player powers in the base game, and 20 in each expansion. Cosmic is a great game, but it is not for everyone. There are moments of backstabbing and cunning plans, there are times where you pull a rabbit out of your hat that annoys everyone else. There are ways to be nice, ways to be mean, and ways to be everything in-between. If you take Cosmic too seriously, you won't have fun with it. But if you're willing to laugh things off and not let a loss ruin your day, it's hard to say no.
Fan of Clue? Here's a fun deduction game that adds a lot of variety and options to that experience. Mystery Express simulates a murder on the Orient Express, except for the ending. Players spend time to investigate 4 categories - suspect, location, motive and modus operendi. Unlike Clue, there are two copies of each card, so players have to figure out which card only has one copy in circulation. There are various means to see cards, as well as trade cards, which makes the whole investigation more complicated. The game takes around an hour, and it's great for people who really like Clue or deductive games.
Power Grid is probably the heaviest game for next level, and because of that, it probably appeals to the smallest group, but in the right group, it's a great game. Power Grid is all about getting power plants to fuel cities, buying the resources to run the power plants, and expanding into cities. You have to balance all three aspects so you're not wasting power, or buying resources at a high price, and certainly so you don't get blocked out of cities. If this all sounds like a big spreadsheet, it kinda is. The thing is, that other players influence things, and change what you want to do throughout the game. I see it as a big economic puzzle, with some key choices on when to do certain things. It is long, roughly 2 hours, but most games are close until the very end.
What's more fun than the Black Death? Well, many things, and that's true of games. There are games that are funnier than Rattus, but Rattus is still a fun game. It loosely falls under the "Area Control" umbrella, meaning that you're trying to have cubes on the board and survive. Through the game, you will use different roles to do different things. Each role lets you do something special, like add extra cubes, make a cube safe forever, etc. but each power you have makes you more likely to lose cubes when the plague hits. For more info on Rattus, read my review.
As you can see, most of these games are fairly pricy. The good thing is, they're fairly hefty games, and you're getting a lot out of them. It all really depends on what you're looking for in a gaming experience. I'd say that Power Grid is probably the best bang for your buck, Mystery Express will probably appeal to the most people, and Cosmic Encounter offers the most variety.
If I have to pick one and only one, I'm taking Cosmic for the replayability.