Hi,
Peak seasons and Golden Week are very busy and it would be wise to reserve your seats - and since they are a free perk with the pass, there is no reason not to. But trains leave every 20 minutes or so, so you should be able to reserve seats (though perhaps not all together as a bloc). If you know what train you are going to take, you can do it all at once at any JR office. You can immediately find which trains are full and which are not.
You can see regular fares, routes and schedules on Hyperdia.
Under "More Options", be sure to uncheck the Nozomi box since you can't ride that train using the pass.
There are fewer people taking Green seats, but there are also fewer Green seats because of that, so it is not necessarily better to have a Green pass.
It is true that those in Japan can make seat assignments ahead of time - but that is because they have tickets - you can't do that until you have one yourself or an active pass, except for JR East which you are not using most of the way (and Dec 25th is not peak season, nor is there any Xmas rush).
You should not have any trouble getting seats on the train if you reserve your seats ahead of time as soon as you activate your pass (and you can designate a future date as your first date, so no problem there). Worst case is you may have to take a very early train and/or not sit all together. To be safe, you should reserve your seats ASAP when you get to Japan.
Good luck.