from what i've been told there is no 777 courses available until the end of the summer, all are booked up till august as it is.
it doesn't matter what your current or last aircraft type is, if you have thousands of hours on a 737 then you will still be put on A330 now. i understand that currently the routes aren't as good on the airbus, but there is the chance of going onto the A380 later on, and when (if) the A350 comes then routes will change and the 330/340 will be gone.
there is currently no one going on to the A380 directly, although i did hear of one pilot rated on it who has gone directly, but this could be speculation, i know, i know, it's not like pilots to spread gossip.
with that all said, please don't shoot the messenger! this is just what i was told during my interviews, i was told things can change any day so bear that in mind too.
good luck to all,
b bear