For a gift, the main things to compare are film format/print size, film availability, and overall ease of use.

If you want prints larger than a business card, look closely at the film size. Among commonly available options, Fujifilm’s Instax line is a safe place to start, and Instax Wide is the larger format mentioned in the answers. The Instax Wide 300 produces prints around 86×108mm (about 3.3×4.3in), which is noticeably bigger than a business card.

Film availability matters a lot with instant cameras. For a casual user, a new Fujifilm Instax camera is probably the simplest choice because the film is widely available in stores and online.

Other options exist, including Polaroid and film for vintage Polaroid cameras via the Impossible Project, plus some specialty products, but those are generally less straightforward than buying a current Instax camera and film.

In short: prioritize a current camera system with easy-to-find film, and if print size is important, look at Instax Wide models rather than the smaller formats.