Unfortunately, accommodation is quite pricey in Japan. The cheapest place to stay that I can think of would be a hostel. I've never been to one myself, but I believe they run around 4000 yen or so a night. Obviously you'll be sharing your living quarters with other people as well. There are also 'bed & breakfast' style places in Japan (usually often shared with other people as well) that can go maybe from 6000 to 10,000 yen per night. These are really your cheapest options - actual, private hotels are not too cheap in Japan
As for transportation, definitely go with the JR Rail Pass. I can't think of a better way for tourists to get around Japan than by picking up a rail pass. Buses are also a decent value - I took the bus all around Kyoto when I visited there - they go by many of the tourist spots.
As for your food question.. eggs, meat, and fish are served in 90% of Japanese meals it seems - even ramen. There are definitely places where you can get a vegetarian meal though, so I wouldn't worry too much. Many restaurants serve noodle dishes that have just vegetables in them.