If it says iOS 5.1.1 is the latest update, that suggests that it is an original iPad (Wi-Fi) or iPad (Wi-Fi + 3G).
You might not ever be able to connect it to the App Store. Early iPads had 32-bit processors, but in iOS 11 and later, all apps use 64-bit code. I'm guessing that Apple made the transition in stages, but that by now, there might not be any 32-bit apps or 32/64-bit apps left in the App Store.
Old versions of iOS might also have used now-outdated security protocols. If the App Store is using a similar kind of security to https Web sites, I could see that being another issue.
On the other hand, I believe that iPad backups used to contain apps, as well as data. If you backed up that iPad on a Mac or PC, perhaps restoring from a backup would get some of your apps back.