Does the library recommend a particular e-book reader for textbooks?
The library does not recommend a specific e-reader, as the world of e-books and e-readers is changing rapidly. You might be interested in this pretty comprehensive comparison in Wikipedia, but the bottom line will be that you should choose the device that feels most comfortable to you.
The future is hard to predict. Many public libraries deliver e-books for borrowing using the Overdrive system, which has worked on most devices other than the Kindle. Overdrive and Amazon have announced plans for the Kindle to include a library lending program sometime this year. This was announced back in April; when it happens it means the Kindle will join the Nook, computers (including tablets), and most smart-phones in the ability to access these loanable e-books. While Harvard Libraries have not yet adopted Overdrive, or a comparable system, it is under discussion.
Part of the reason for hesitating over investing in the Overdrive formats is that publishers are not entirely certain how they want to proceed with borrowable e-books. Some don't do it at all, some only in a limited way. In addition, we can't say for certain that any particular hardware will continue to be compatible with any particular software. So, for instance, Apple and Amazon have a Kindle app right now, making Kindle formats readable on iPhones and iPads, but either one could end this arrangement at any time.
Since tablets can do what dedicated e-readers can do and more, they are generally more versatile and future-proof than things like the Kindle and Nook. The downside of using an iPad or Android tablet is that they are more expensive, heavier, and their battery life is limited to a day or two. It is also difficult to read their screens in bright sunlight. Some people just prefer the ergonomics of the dedicated readers.
Since many textbook titles in e-book format are too large to be read on a Nook or Kindle device, the Harvard Coop recommends a software application called Nookstudy that you can install on your laptop or tablet and use to manage your e-books. You can learn more about it at nookstudy.com/college.
In the end, it will come down to personal preference, with, unfortunately, no guarantee that your choice will be capable of all you may want it to do in the future.
See also MIT's E-reading FAQ.