Because of the way our training freezes work it is extremely unlikely that a new pilot would ever get the 777/787 as their initial assignment. However, getting a bid to one of those fleets while in your first year is a possibility.
Basically you will get your first assignment on either the 737,A320, or 756 fleet. With that you will be "frozen" from bidding within the same pay band or down in pay band for two years. This does not prevent you from changing to a different base, but does prevent you from bidding from 737 over to A320 or A320 over to 737. If you get the 756, you can lateral to other bases, but you cannot bid to either the 737 or A320 for the length of your freeze.
Now, that freeze does not prevent you from bidding up in pay bands. So, if you get the 737 as your initial assignment and a new vacancy bid comes out while you are in your first week of new hire class, you are eligible to bid for not only a lateral to a different base, but also any 756FO assignment or 777/787FO assignment you would like. For this reason there is always a chance that a 777FO assignment could be snagged by somebody very early in their time here.
So, the least restrictive initial assignment would be to either the 737 or the A320 and in either of those your QOL will improve more quickly as will your ability to lateral to a different base you may desire. The 756FO slots will also still likely be randomly available as initial assignments for the coastal bases as we go forward. An initial assignment to that fleet would still allow bidding up to the 777/787 and laterals to the other 756 Bases (IAD,IAH,ORD,DEN) However, the fleet itself is smaller and the 767-400 pays better, so when folks get senior on that fleet they may never leave, thus the movement is slower.
As far as the 777 goes, the junior bid holder on that fleet is about 750 seniority numbers from the bottom of the list. The next vacancy bid will come out at the end of July and close in early August, so that will give us our next update on how junior things will go. The next few bids will have Fall/Winter training dates as their target, so unfilled assignments on these vacancy bids will be what is used for the Fall classes
The good news is that movement is crazy right now, so you will have many options (once you actually get hired and start!!) However all this movement does make me obligated to bring up the old bidding guidance:
Bid what you want
Want what you bid
Careful what you bid for because you just might get it!!!!