My favorite ones I've done:
"Self Sufficient" - No purchasing any items which will then go into your inventory. So upgrades are fair game as are animals and buildings, but no purchasing food, wood, stone, seeds, or anything else which will go into your inventory as a result. Not even heaters or a milk pail. It's entirely possible to get the community center done this way for what it's worth, and it can be fun to figure out how.
I also have done and recommend going with things that are not the typical crop route, here's some examples:
"Flower Power" - The only goods you can sell or gift to others are flowers and flower byproducts. This includes the flowers themselves, honey, mead, and oil from sunflower seeds. I did the Joja route on this one but if you want to do the normal community center you would just need to make sure you're not selling or gifting other crops etc and only throwing away any excess beyond those needed for the bundles. Would personally recommend going Joja though so you can go more "pure" flowers.
I also did a Maple Syrup farm which was less a strict challenge and more just a theme, I think these days you could do even better with a "forage farm", foregoing traditional crops and focusing on only things that grant forage XP or no XP. There's the syrups, wild seeds, truffles, and more.
Currently I'm doing a "cropless" run as I try out the meadowlands - not planting any crops at all, going pure rancher. So far it's been fun.
I also think it can be fun to focus on collection based challenges -
"Ultimate Fashionista" - Collect in a shed 1 of every clothing item which exists in the game. Easier said than done!
"Ultimate Fisherman" - I made an aquarium with an iridium quality fish of every variety. Quite the challenge with legendary fish, next time I do it I'll be going for 3 iridium quality legendaries since the challenge bait allows that to occur, as well as at least 1 of everything else.
Just a few ideas for you, the most important thing of course is to do something you find to be fun! Good luck and enjoy!