Train Travel is definitely the best way to get around Japan -- efficient, clean and quick. Hard to beat! The downside -- train travel is so well used and is such a part of the culture that it can be the most confusing way to travel around Japan as well. Some pointers:
Shinkansen or Bullet Train
As you two already know, this is by far the fastest way to get around. The train is so fast that it has it's own special train tracks and very limited stops. It also by far the most expensive way to travel and really only goes to main tourist hubs. If you want to get out and see "Old Japan" you will have to get off the shinkansen.
Limited Express (aka LEX)
In speed, this is the next step down from the shinkansen. It uses the same train tracks as other local trains, but usually makes very limited stops and will skip several train stations. (Warning: if you are going to an off the beaten path train station -- make sure that your train actually STOPS there!) Seating is spacious and comfortable and for long journeys this is the way to go. You will know when you are riding a LEX b/c you will be given 2 tickets. One is the normal fare charge and one is for the "limited express" surcharge.
Express, Rapid and Local Trains
Everything else falls into this category. Don't get "Express" and "Rapid" confused with "Limited Express". Again, the key is if you've paid a surcharge, you're on a LEX. The "Express" and "Rapid" trains are actually just local trains that skip stops. You pay the same fare whether you take a local or an express. If you are on a budget, look for express and rapids. They can sometimes be as quick as a LEX but w/o the surcharge (often adds between 20-50% more on the normal fare). You do give up comfort (the trains are usually much more crowded) and space. If you are travelling a long distance and with luggage -- stick with the LEX.
Confused yet? Bottom line - for short distances or for sightseeing, look for rapids and express. They usually run more often and are cheaper. For long journeys which includes luggage (i.e. travelling to your next overnight destination) look for the LEX. They are worth the extra $$.
Some other thoughts...
Luggage - Travelling in Japan WITH luggage is a pain. There is just no way around it. Train stations often don't have escalators or elevators and the trains are not designed for large pieces of baggage. Not only that, but Japanese DON'T travel with luggage so they'll stare at you. Whenever you can, get rid of your stuff. There is a luggage forwarding service called takkyubin that I've never actually used but wished I had researched it more before we left. Also there are lockers in the train stations but it's very inconsistent and often full. If you're going to a very remote location, I would recommend leaving your luggage behind and coming back to get it.
More than just JR - You may be surprised (I was) but there are several other train companies other than just JR. If you have a Rail Pass, you'll be looking to travel on JR as much as possible. But oftentimes (again for the more remote locations) you may have no choice but to travel with another company (i.e. Nankai). Don't let this throw you -- also, keep in mind that although travelling on JR may be free (again, assuming you have a rail pass) the other train company may be quicker and worth the extra cost.
Train Planning - When I was in Japan we were travelling to a new town every 2 days. Yes, A LOT!! We got into the habit of mapping out our next destination almost as soon as we arrived. Picking up train schedules, asking questions, etc. If you know what your next destination will be, it is worth it to do a little planning. Especially if you want to use the LEX.
Ok, that's it for now...hope this helps. I'm looking forward to reading your next dispatch!