Amenities usually cost a whole lot more resources to build when compared to Furniture. Plus, the time needed to construct them is just as long. When you pick an amenity to build, Cyrus will also immediately ask you where you plan to build it and will then cover the construction site until it is ready to be unveiled. Once the amenity is built, there is the option though to move it or replace it with another one. You also get build one amenity at a time -- unlike that of furniture where when you purchase the 2 additional slots, you get to build 3 furniture at a time.
Once you've built an amenity, you'll earn its benefits permanently in the game regardless if you choose to remove from your camp or pick another amenity to build in its place. What this means is that if you have unlocked a Cap Level of certain types of animals in the game, it will remain unlocked even if you put the amenity away or change it with a new one that is (for instance) meant to unlock a cap level for other types of animals. Additionally, its effects are not limited to the animals staying at your place -- which means even if they are sent home for instance, they'd permanently gain every increase the amenity is suppose to provide. The same is true with all the animals (of the same type that benefits from the amenity) that are yet to be friends with you or that are away when you've built the amenity. When they visit your place even after the amenity is gone (replaced), they would still be affected by its benefits.
The additional benefit that only present animals in your camp earn is the +5 Friendship points they get whenever they are invited in the unveiling party. Hence, if you happen to have animals which do not benefit from these points (for instance they've reached their currently cap levels), you may temporarily send them home and invite ones that would benefit from it before you proceed with the reveal. You get to suspend the reveal until you go to the Crafting menu and clicking on the pertaining item.
Lastly, you'll want to check all your current animal guest/friends first before investing/purchasing Amenities. Basically, there would be a majority of a specific type (of animals) in your camp. If you happen to not know how to view your animal friend's type, just go to their profile in the "Contacts" button, to see their "Preferred Theme". You might want to invest in amenities that would benefit more animals first, or at least the ones that you'd want to increase their cap levels first. Build the basic amenities (four of them), and then upgrade them accordingly (just as you weighed down which should go first when you initially build them).