Illustrator's drawing capabilities are closer to Photoshop, but 'better' for non-raster illustrations. It's also widely used in printing, but not for multipage documents like InDesign, as it has no support for master pages and it doesn't let you automate page numbers.

Illustrator is used for illustrations, logos, and scalable graphics in general. So, you could use Photoshop, but then you'd have issues preparing the files for the printer. Think of it more as a way to edit pictures you want to then add into printing materials. Its main 'power' comes with its image manipulation possibilities. Photoshop is best for creating and editing photos or raster images. Yes, you could use InDesign, but you will be missing drawing features. The good thing is: It packages fonts and images all in one file, but the file size will generally also tend to be bigger, so in your case, it might be a bit of an overkill. However, where it shines is with multiple pages (tools like text wrap are extremely powerful). That's its strength, you can see it as a way of joining Photoshop and Illustrator elements into a new 'thing'. InDesign's specific purpose is laying out printed materials. If you have the time, I'd definitely recommend you pick one (spoilers: It's Illustrator). While the three Adobe products have some similarities of use, they all require some learning time. If you are particularly proficient with one of them, you might want to consider going for that one to save time. In theory, any of those (plus others you haven't mentioned, like the open source alternatives Gimp and Inkscape) let you design a business card.

Indesign vs illustrator