Here's my take on all this.

I don't know your itinerary, but if you are going for 17 days, my guess is that the 14 day may be best for you, not the 21 day pass, unless you are planning long train journeys in the first few days of your trip and again at the very end.

The difference in price appears to be about $120. You should be able to structure your itinerary so that you've got three days either at the beginning or end when you'll be spending less than $120 on JR trains over that 3 days period.

If you're flying into Tokyo and sending at least three days there, you probably won't spend $120 over those three days on JR trains, because you'll be using the metro around Tokyo, and even if you use JR trains within the greater Tokyo or Osaka areas, the journeys aren't too expensive. So you could fly in, spend 3 days around Tokyo, then activate the 14 day pass on day 4.

Or alternatively, fly in to Tokyo, immediately activate the 14 days pass, use it for the Narita Express, etc. and then just pay out of pocket for trains over the last three days of the trip when you'll be in and around Osaka.

The expensive trains are the long distance shinkansen trains. You'll want to avoid paying out of pocket for those if possible and putting those journeys in the first 14 days of your trip or in the last 14 days of your trip.

You can activate it for any day you want. In the major cities, I used a mix of JR trains, private non-JR local railways, and (most commonly) metro. Traveling between cities, I used the JR trains. I hope that helps.

The trick is to consider how much travel you would cover with the Rail Pass and how much it would cost without a Rail Pass, not how long you will be in-country.

If you will be spending most of your time in Tokyo at one end of the trip and Kyoto/Osaka at the other end, with little train travel in between except the one-way shinkansen (bullet train) between the two plus the one-way trips to and from the airports, then the Rail Pass would not save much if any money over just buying tickets as you go. In that case, I'd forego the Rail Pass and just get a pre-paid travel card like Suica that would cover subways, local trains and such.

On the other hand, if you will travel extensively outside your two major destinations by train in addition to that mentioned above, it might well make good monetary sense to have a Rail Pass. Side- or day-trips from the main destinations can add up. If you plan to get out of the major cities and go places like Nikko, Matsumoto, Himeji, Hiroshima and other great locales, then rail costs can add up and a Rail Pass would be a good idea. The rule of thumb for the 7-day ordinary Rail Pass is that it begins to pay for itself if used for a round-trip Tokyo-Kyoto-Tokyo PLUS a one-way to/from either NRT or KIX. Anything over that is gravy. For the 14-day Rail Pass, you would need a lot more travel to pay for itself.

The Japan Rail Pass is a great investment for those contemplating a lot of long-distance rail travel between cities. It is of little value during a stay in Tokyo, Osaka or Kyoto as those places don't really use a lot of JR lines. They have subways, buses and local line trains, none of which are covered by the Rail Pass. Unless you are planning a LOT of running around the country during your 17 day visit, I can't imagine the 21-day Rail Pass would be worth the cost. If you will be staying in Tokyo for at least the first (or last) 4 days of your stay, then the 14-day Pass would likely suffice. Just pay cash as you go for the other 4 days. I have traveled extensively all over Japan and have never found the 21-day Pass to pencil out for me. I just couldn't cram enough rail travel into my 2.5 to 3 week stays.

Plan your visits and stays, try to arrange the longer travel within a 7- or 14-day period within the 17 day stay and then decide which Rail Pass would make economic sense for you. If you pay out of pocket for the trip into the city from NRT and stay in Tokyo for the first few days, the 14-day Rail Pass would likely be all you need.