Well, they don’t minimize luck, but they shift the location of it in the process.
For example, in Carcassonne, there’s plenty of luck involved, in the process of selecting tiles to place. Nothing like needing that one tile you know exists and getting it, thus completing the city exactly like you wanted! BUT, after the luck, you are in general presented with choices of what to DO with the luck. So, imagine if in Monopoly, the properties were distributed more randomly as to what was more valuable, and after you roll, you get to choose which direction to travel. I remember a game from the 60s called Careers, where you did Monopoly-like play (travel around the edge of the board in a single direction), but you got to make choices about what “career path” you would choose, which caused you to veer off the main track, and which altered how the game played for you then on. I always preferred it to Monopoly for that reason.
As for the OP, the usual suspects are Carcassonne, Settlers of Catan, and Ticket to Ride. All three are winners of the Spiel des Jahres, a prestigious award given out in Germany to “family-style” games (primarily board games). This award is the genesis, if you will, of the “German-style” board game; it rewards games for concept, structure, layout, and design. So each of the three games above are excellent games, as determined by the critics which make up the panel of the Spiel des Jahres voters.
In addition, they all are relatively simple to learn, have a limited amount of time they take to play (for example, when you run out of tiles in Carcassonne), and have simple scoring rules. They all force you into both strategic and tactical choices. And they can be played, and enjoyed, by both young and old, together or separately.
Since you’ve eliminated Catan, it would help to know why. If you’ve eliminated it for complexity, then I would recommend Ticket to Ride over Carcassonne, as the latter is a bit complex, especially if has any of the expansions added. But one good version of Carcassonne that is especially kid-friendly is called Hunters and Gatherers, which reduces some of the complexity, and I find can be played much more quickly, even though it’s otherwise essentially identical (tiles chosen and placed, units then placed on the board to maximize score). Got my kids hooked on Carcassonne, and generally on German-style games with that one.