So please do take advantage of this holy holiday. The custom is to stay up all night learning Torah. If you can't stay up all night than just push yourself as much as you can and you did your best. There is a custom of eating dairy meals on Shavuos. There are many allusions to this in the Torah.
Honey is understandable.
Making milk a very appropriate symbol for again receiving the Torah for the first time. Knowing that milk symbolizes the sweetness of Torah, it's not too difficult to see meat, that which milk should never come in contact with, as symbolizing materialism. I've heard it said, but have not seen it written, that on Shavuos and Shavuos alone, some have the custom NOT to wait the usual 6 hours if they've had meat and are wanting to eat milk. This would be the opposite of what meat represents. Judaism takes extra efforts to separate life and death.