From the perspective of how much you individually could read in a lifetime: that's about 4,000 weeks (to roughly age 80-ish, and presuming you're not already reading at birth). Multiply that by the number of books you plan on reading a week. You'll probably read fewer than 4,000 books over your entire life. Many people read few if any books after graduating secondary school, and even a highly-motivated reader might be challenged to crack, say, 40,000 (ten per week for life).
The US Library of Congress has the world's largest book collection at about 40 million distinct titles.[1] There are another 130 million total catalogued items, including photographs, films, audio recordings, maps, pamphlets, and other items. Not all are textual. I'll stick to books.
At 4,000 per lifetime, you'd need 10,000 people simply to read all of the LoC's collection at a reasonable pace.
(By comparison, at the turn of the 20th century, the LoC's annual report to Congress noted that its cataloguing department could handle about 3,000 books per cataloguer per year, or a pace of about 60/week or 15/day. Over a 40-year career, a cataloguer might handle, if not read completely, 120,000 books.)
As a rough rule of thumb, a digitised ebook in PDF format runs about 5 MB.
Every single book in the Library of Congress in digital format would occupy about 200 TB of storage.
Current disk prices are running about $5 -- $20 / TB.
200 TB in raw disk would set you back $1,000 -- $4,000. Figure 2-4x multiplier for a disk storage system all told, and it's still roughly $4k -- $16k to have as local storage every last book in the US Library of Congress. That's well within scope of a moderately wealthy US household budget, and would be reasonable to consider for a small-town city library.
That's the technical storage cost, obviously not the rights or aquisition costs for the materials.
The Library of Congress's budget is about $800 million/yr.
Those 4,000 books you might read in a lifetime? They'd fit on about 20 GB worth of disk. If you're a 10x reader, 200 GB, and a truly dedicated 100x reader, about 2 TB. Those are well within the range of present desktop / laptop disk allocations, and represent a few tens of dollars of storage expense.
The Internet Archive computes $2/GB for storage in perpetuity. That's roughly 400 books worth of storage.
But a small household NAS and a very modest server platform (most routers can effectively operate as media servers) could rival a mid-sized city library for about $100 or less in actual hardware outlay. Those prices are falling by half about every 18 to 36 months, as they have been for decades.
Books are not all published content, and all published content is not all human knowledge. But standard published books are a good proxy for total cultural knowledge, and in all likelihood, then some.
________________________________
Notes:
1. See: https://www.loc.gov/about/general-information/ That includes about 25 million books in the main collection, and 15 million in "nonclassified print collections, including books in large type and raised characters, incunabula (books printed before 1501), monographs and serials, music, bound newspapers, pamphlets, technical reports and other printed material". I suspect you could roughly halve my estimates above based on 25 million vs. 40 million volumes, as many of the nonclassified works may duplicate the main collection.