As others have mentioned, scanning isn't a problem, and the software needed to run your scanner needs very little horsepower or RAM.
But...you will soon find out that doing some 'touchup' is always needed, especially for older, faded photos. I recently did perhaps 200 photos for a friend and every one of them (95% were B&W) needed some sharpening and a bit of extra contrast & exposure adjusting to make them look good. So the issue becomes RAM and horsepower. I'm using Photoshop Elements and can hold maybe 15-20 pictures in RAM that were scanned in before it starts swapping it out to disk (paging). So, I simply scan that many in, then do touchups and save each, then start over with the next group of 15 or so. Since I'm editing, a quad processor computer is strongly recommended as PSE and others can likely take advantage of the multiple processors. Also mentioned previously was using a Solid State Drive (SSD) as it's far faster than 'regular' hard drives. I use SSD for the operating system, documents, and any work 'in process'. I also back up the work in process to the slower 1TB hard drive that is also in the computer. Using SSD speeds up all computer aspects from boot up, program start up, and retrieving/saving files. It's well worth the extra $$$ in my estimation.
For what it's worth, when I built my computer, I'm not interested in game-speed graphics, so I have a cheapo video card that's good enough for me. So if it takes a 1/4 second longer than some $500 graphics card to display an image, so what. I think I paid $39 for mine 2 years ago.