How does Rook compare in difficulty to other trick-taking games?
It is commonly played by older people in my area, and so my siblings and I learned it as small children.
What games would be good to pick up, having that background?
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Of all the other card games I know, Rook is most like partnership Whist, with only a few exceptions:
Tournament Rook uses the rook-bird card, which serves as the highest trump card (not a wild card: the rook-bird play still must follow rules of following suit)
Bidding in Tournament Rook is done by point counting, not by trick counting (as with Whist): fives are 5, tens and fourteens are 10, and the rook-bird is 20. (As with Whist, trump is not named until after the bidding has passed out.)
Tournament Rook sets aside a "nest" of five cards on each deal-out that is not used by the players to play the hand, nor are the cards visible. This gives each hand 10 cards. The winning partnership counts the points in their won tricks, plus any tricks in this "nest".
The two aspects of the game I like most (and which make it more interesting than Whist) are the "nest" and the separation of bidding and measure of "successful play" from the number of tricks captured.
There are plenty of other card games that assign point values to cards and both bid and measure success based on those cards (Mü, Skat, Tichu). However, I can't off the top of my head think of other games that also incorporate a kitty of cards taken out of play that get assigned to the winning partnership at the end of play.
I'd say that it's among easier trick-taking games, but not too simple. Games of similar difficulty would be Spades, Euchre, and Pinochle. Hearts also works, but you'd need to remember it's about avoiding taking points. None of the games have anything similar to the rook card. Spades, Euchre, and Pinochle each have team play with the option to "go it alone". Spades has a set trump suit. Euchre and Pinochle use modified decks, and both change card ranks depending on the trump. Pinochle is the hardest of the three, with a melding phase.
An advantage of mini-bridge over rook/spades is that it's deeper, but equally easy to learn the rules. It also gives you a lot of upside in that you could move onto playing Bridge, which is the classic among trick taking games: more complex, more fun, and more rewarding.
Mini-bridge is being taught as an alternative to Chess in many schools among younger children, with the idea that they'll move on to play the real thing.
There was an answer deleted that had a good link with a complete answer, I'll repeat it here.