I really nice encapsulating beginner challenge is to try and complete the community center in a year (or two years, or even by the second summer so you don't have to deal with the red cabbage messing with you).
I've found you can really make a challenge out of anything. Pick something you like in the game and focus on that, or try going entirely without your favourite part of the game and see how you fare. This could take the form of an animal challenge where you try to make most of your money from lots of animals, a fishing challenge, a challenge where you avoid planting crops, a challenge where you try to cook as much pizza as possible.
You can add some sort of natural end or goal to reach for like how many pizzas by year 2 or how long it takes you to make 1000 pizzas (very stuck on that example seemingly), but you could just as much not, and just play and enjoy having a rough guide for your journey rather than destination.
Have fun with it!
