If this signing up is done on a website, using a browser, and if the building has wifi, then it could be done with an Android tablet. Google 'Android tablet less than $100'. You'd need to check that the website works with the tablet's browser, which might be peculiar to the manufacturer (e.g. Amazon's Fire tablet uses a browser called Silk).

The printing requirement is probably the trickiest. There is no standard. I use a Brother wifi-connected printer and a Brother printing app on this Google Android tablet, but I'm sure other solutions exist.

Any manufacturer's device can access wifi.