I will differ a bit.
Depends on your overall design.
Infographic is a pretty board concept, it could include for example dozens of photos representing a taxonomic chain for example, but in your description looks like you only want to add some text on each poster of each animal.
1. If you only need a couple of images in your poster, I would use Illustrator. This will allow you to add the text easily and add some additional elements, some icons, vector based borders, extend your black background, etc.
Illustrator can handle well several raster images, especially if you link them, not embed them. Take a look at this link to keep your illustrator file small https://forums.adobe.com/thread/679995
2. I would only use Photoshop to make adjustments to your images, but as commented, Photoshop has several ways to work with the images maintaining some "scalability" so you have the flexibility to print a large poster or a smaller one.
3. If your infographic does include several images, for example, more than 10 I agree that the best option is InDesign. All the photos in InDesign are linked externally by default.
InDesign can be an interesting option if you want to produce a "series" a collection because you can have a "Master design" and you apply this design to consecutive pages, like a catalog. You can have all the collection as several pages and print just one, or the entire collection.