Well if he is going to get a smart phone, I would highly recommend an iPhone. Apple is leaps ahead of any other phone when it comes to accessibility. As for as the tutorials, I'm not sure to be honest. Facebook, I don't use it anymore, but I'm pretty sure it's usable. Though I know for a fact it's usable on an iPhone. Hope this helped.

As for Facebook on desktop, many people use the Mobile site at http://m.facebook.com. It doesn't have all of the features of the regular site, but is often more efficient for quick posting of status and doing other common FB tasks. Yes, if you haven't bought Jaws yet, NVDA is a better option for the web and free. You can buy better-sounding voices if the built-in one sounds a bit harsh, or if you're on Windows 8, switch to the decently-sounding Microsoft voices. Those Nokias were good phones for their day and until the iPhone, one of the only accessible smartphones available.

Smartphone: Unfortunately I don't personally know any blind Galaxy users but everyone who I know who uses a touch screen phone is successful in navigating their phones. There are books available in various formats including braille and Daisy that give you instructions on how to navigate your iPhone and what Apps you might find useful.

You can also find information on using Android while blind $1

The Internet: Again there are books on how to navigate iOS and Windows computers in various formats. There are books on how to use google, and how to tweet, and emails.

$1 are some of the publications that we carry.

Facebook is pretty easy to navigate blind - some practice and it works on iOS.
I use VoiceOver & other vision accessibility settings.
Iʻve never used a Samsung, but Iʻd imagine they would also have some good accessibility settings

I would not recommend giving him the old Note phone. A note 3 or 4 would benefit him much, much more. The much older forms of Google's talk-back, kick-back, and sound-back are going to work yeah, but it's going to frustrate the hell out of him.
I'm using a Galaxy S 6 and no disrespect to apple users but being fully blind Google and Samsung aren't so 'light years' away any longer. I''m fully blind and I can vouch for the mobile facebook being tons better than screen reading on pc. It's simplier to use, which is the goal for accessability.
As for the jaws tutorials, well, weather it's an i-device, which by the way even the old ones are much more expensive, or some mid-range android device, the youtube app works for almost all platforms. I played with the search and there were tons on youtube, how to turn on, use, etc etc.
If nothing else, you could always get a tablet to introduce him to mobility. A nexus 4 are relitively inexpensive, and still somewhat modern enough for learning and teaching.
I hope this helps.

Facebook on the computer has improved a lot, over the last year or so. But it uses all the fancy new accessibility APIs, so if your version of JAWS is even 1 version out-of-date, Facebook is going to be a lot easier on Mobile. Think of it like this: on a computer, you have a large screen, with lots of memory and CPU, so apps are designed to have multiple things happening, all at once: a scrolling activity feed on the side, chat messages and notifications popping up, an endlessly scrolling newsfeed, and all that just on the one page, not counting all of the other apps the computer is running. On a phone, the screen, CPU, battery, data, and memory are limited enough, that most apps are designed to only do 1 or 2 things at once. As a 27-year-old blind person who has been an extremely active computer user since age 9, even I find doing a lot of things on my phone much easier and less frustrating.

If you do want to keep your grandfather on the desktop, I strongly recommend getting him using Firefox with NVDA (http://www.nvda-project.org). NVDA is a free and open source screen reader, so he can have the latest and best, without having to pay several thousand dollars every 2 years. Also, currently NVDA's support for web apps, when using Firefox, is the best by miles. The key commands are similar enough to JAWS that he won't be totally lost, either. Also, once you've gotten him on Firefox, you can give him AAdBlock. For a blind person, this is the best thing. First off, it blocks all of those animated ads and pop-up windows and spammy links with no relation to what we're trying to do. This will make the screen reader faster, and his experience much better; as a blind person, it's sometimes not obvious where the ads end and the real website begins. And if you know a little about web development yourself, if your grandfather finds something on a website difficult or confusing, you can use AdBlock to get rid of it for him, or GreaseMonkey and Stylish to modify it. This is something only Firefox seems to allow, and in my opinion, is another reason why Firefox and NVDA leads the pack in accessibility.