Today, I finally got two items I wanted to get for some time. A commuter pass and a PASMO.
I got a student commuter pass from Seijogakuenmae to Shinjuku, for the Odakyu line. This covers one half of the route to the Hongo campus I have to take three times a week, and it also covers the route to my lab (then I get off before Shinjuku, but that doesn't matter, it still works). Plus I can use it whenever I need to go to Shinjuku for something else (and since that's usually the first stop no matter where in Tokyo I want to go, that happens a lot). Despite the fact that most people told me I couldn't get a student pass as long as I was only a research student, I still managed to get one. Which is good, since it's a good deal cheaper than a regular commuter pass. I waited so long to get one because I wanted to at least try to get a student pass, so I had to wait until I had my student ID card.
I considered also getting a pass for the second part (from Shinjuku to Hongo-sanchome with the Oedo line), but I only do that three times per week, and there's far less chance of incidental trips that way than on the way to Shinjuku. The commuter pass would cost almost as much as the single tickets would, so I didn't do it. Plus this affords me the freedom of using alternative routes, such as the Chiyoda line, if I want to.
It should be clear from this little explanation that the biggest problem with Tokyo public transportation is all the different companies. You pretty much have to buy a ticket every time you transfer. So far I've been using a passnet pass, which is a magnetic ticket which you buy in advance. It's not any cheaper than individual tickets, but you buy a fixed amount in advance and can use the pass until it's empty (then you must buy a new one). Passnet works on Odakyu and most subway lines (including the Oedo and Chiyoda lines), so it was fairly convenient. It does not, however, work on the JR lines. JR uses a system called Suica, which is a rechargable IC card (chip card), but that doesn't work for anything besides JR (or at least it used to).
A few months ago they introduced the PASMO. It's a rechargable IC card which works on (afaik) every single train and subway company in Tokyo (even JR; the PASMO and Suica can be used interchangably) and even in most buses. Like Passnet it's not cheaper but it is considerably more convenient. What's more, you can also put a commuter pass onto a PASMO, so I can now use this one pass where ever I go in Tokyo, even for the commuter pass route!
I would've gotten a PASMO a great deal sooner, but the PASMO was far more successful than originally anticipated (apparently they sold over 3 million in the first month; they had predicted only 2 million). Because of this currently PASMO's can only be bought in combination with a commuter pass; "normal" PASMO sales have been halted. But now I have one, which will make things much easier. :)
PASMO official site (in English).