As mentioned, you can get decent scans with the Google Drive app if you use basic photography techniques.
The Google Drive app does perspective correction on the image, turning your snap from trapezoid to a rectangle, so it's ok to hold the phone forward or to one side.
You can improve the image quality with more light and by steadying the phone - take the pics near a window in the middle of the day and use a cardboard box or a stack of books to rest the hand holding the phone so it doesn't wobble about.
Eventually I just gave up and bought a Doxie Flip portable scanner.
I used to like the Canon Lide flatbed scanners, but had to keep replacing them because Canon's Mac drivers became obsolete after a few years - I managed to get two or three free from friends and Freecycle.
The Doxie Flip is a small flatbed scanner, but it doesn't require a PC - it just saves the images to an SD card, and then you can copy them off the SD card onto your phone; it runs off AA batteries, so you can use rechargeables. Unfortunately the scanner is A6, a quarter the size of A4, so you have to move it around the paper and then stitch the images together afterwards - Doxie provide software for this, but I believe it's based on an open source program (Hugin?), so one shouldn't be dependent on them.
I absolutely wish that Doxie would make an A4 version, but the Flip is a convenient size if you live in a small space and it scans reliably once you learn the knack of moving around and taking enough scans to ensure the whole paper is properly covered.
Having read your question again though, it sounds like you have quite a considerable volume of documents to scans so it's probably not suitable for your needs - the multiple scans required for A4 are far too much faff for more than a few pages.
In your position I would contact all the local professional document-scanning services and ask for quotes. How many pages were you able to scan in 30 minutes at the library? It sounds like you have 10's of hours of work ahead of you, and these guys have machines that can probably do 50 pages a minute; the may be more affordable than you expect. I know this sub is about saving money, but how much is your time worth? Any least get a few quotes.