Epub is the most broadly supported of the bunch. It should work on just about any dedicated e-reader except an Amazon Kindle. They often come with Adobe Digital Editions DRM which is fairly widely supported. A few books stores (like Barnes & Noble) use their own DRM which will generally only be supported by their reader hardware and apps.
The Amazon Kindle books will work on a Kindle, but not on any other dedicated e-reader. They come with Amazon's own DRM.
Epub and Kindle reader apps are available for most tablet and phone OSes.
I don't know much about iBook. I expect it is comparable to Kindle books in terms of compatibility at best.
So if you don't think they'd be interested in using an e-ink reader in future, the amazon or e-pub methods would both work. If the e-pub is DRM free, that's a clear winner and yes you'll be able to just give them the file with no hassle then. A Digital Editions epub or a Kindle book will probably require that you give the book through the bookstore somehow.
If you do think they'd like an e-ink reader, then you can give them a book that works on one (Kindle), or all but that one (DRM free or Digital Editions Epub).
Instructions there. You can just set it up to email to them at the time you're planning to be at their house. Then just buy a nice card with a short explanation of what to do. If they don't want the book or already have it then they can exchange it for amazon credit. Also, it works well with the iPad, mac, pc and I'm fairly sure it will work with most all droid phones.