A few suggestions on inexpensive framing options:
I like the Ideal Bookshelves best in white wood frames, and the best off-the-shelf ones I’ve found are West Elm’s gallery frames. I also like IKEA’s Ribba frames. They both also come in black and silver, in case the white is not for you. They have great rectangular ones in various sizes, and even nice square ones that often fit the paintings with fewer books (7 or so) perfectly.
Unfortunately, the mats that come with the frames usually have too small an opening for the bookshelf images (especially for the West Elm ones; the IKEA ones are more straightforward). But you can get a custom white mat cut for you at most art supply and framing stores; it usually costs $10-15 at most. Some places may even just cut the opening on the West Elm mat larger for you, to fit the image.
Hope that helps! Also, this video from 20x200 does a great job showing how to do all of this yourself.