Bluefire Reader 4+

I've tried all kinds of e-book reader app and this is hands down the best. It opens every .epub and .pdf I've ever thrown at it, and loading the books onto your iPad through iTunes is easy peas - just drag and drop all your books onto the Bluefire icon in the file sharing section.

The book title/cover display section is clear and easy to read, books load quickly, the fonts are great and you can adjust the size, and you can create your own bookmarks. Bluefire Reader is really well designed and, amazingly, it's free (although you have to wonder what personal data the developers are getting, because free apps are almost always out to harvest and sell your personal data).

Anyway, that aside, this is the best e-book reader for iOS by a mile!

I like the Bluefire reader app and have been using it to read library loans for nearly five years now. You can alter the size of text and the font, and I especially find useful the "night mode" button that lets you read in bed without disturbing your partner.
The only gripe is that choosing a book isn't always easy, navigating the filters and genres, and the synopses of the books are always truncated, so you don't always get a flavour of the book in question.

UPDATE

I haven’t used the app so much in the past few years since discovering Kindle Unlimited, but I still have a very large collection of my earliest purchased e-books stored with this app as they’re all Adobe digital editions. I recently fancied re reading a series from my collection but gave up after book one as it was so slow to turn the pages it just made the whole process unpleasant rather than the joy it should be, to the extent I even looked into how to move them to a different app, unfortunately it seems that due to Adobe I have no other options.

The addition of being able to create your own individual 'collections' is something that I have been wishing for almost since first using the app. It has made this so much easier for me to use as well as being a lot quicker to load.