The fastest, easiest way.....
Create a new InDesign document the same page size as the PDF. Place each PDF page on an individual InDesign page. Then draw your white box and new numbers.
You could use Illustrator or Photoshop as well.
Although, in general, I'd suggest not using Photoshop if you got the PDF as a PDF from somewhere, since it will rasterize everything, making one big image and dumping any vector data. But of course, if you scanned the file it's already raster so that won't matter. i.e. some copiers can scan and save as a PDF and email... these are just raster images so Photoshop may be better than Illustrator for these types of files if you want to actually alter the PDF data.
Illustrator is a viable option if the PDF came to you as a PDF exported/saved from some application. It just means you have to alter each page of the PDF. If you actually want to change the PDF data, then Illustrator is the best option.
By using InDesign, you basically just accomplish what you are doing via comments in Acrobat. You don't alter the original PDF data, and merely cover up what you don't want to print. You also get one InDesign file as opposed to multiple Illustrator/Photoshop files or an Illustrator file with multiple artboards.