Shinkansen Guidelines
So, you could hop on without a reservation... but if you're afraid that the train might be too crowded before you take it, you can go to a JR tourist office to book a seat. Note that this office is only in the North Gate of the Tokyo Station.
Know that there are three tiers of fastness, but JR Rail Pass holders aren't eligible for the fastest trains. Keep that in mind when you look at the timetable.
It will be confusing to find your way through the station. If you're going towards Kyoto from Japan, follow the signs for the Shinkansen, and then there should be a big timetable up with track numbers. When in doubt, most of the folks in the Tokyo station who work there know English, at least at the ticket counters, so feel free to ask them stupid questions.
Yes, you can (surprisingly) fit a decently large suitcase above your head on the rack. However, I saw some folks with bags so big I'm pretty sure I could fit into them. My point? Any bigger and then you have to tell one of the conductors that you need to put it on the rack in the back of the car. My advice? Travel light. Japan is so much more fun with a backpack. Between multiple flights of stairs for shrines (I literally saw "bag drop" rental areas near the Fushimi Inari shrine) and subway stations, roller bags are a really bad idea if you want to get around quickly.
The bento boxes are really good (and not terribly overpriced). I bought my lunch for about $10 USD. I thought it was a hard boiled egg but was really surprised (and excited) that it was a softboiled egg, instead! There's a nice kiosk on the platform where you can buy your meal before boarding.
There is a snack and drink cart lady who passes through the cars, but since I didn't really get a chance to see what she was offering, I can only tell you that she for sure has tea and coffee pots.