I played through the prologue (hospital stuff) and i get stuck at this install screen. there aren't any prompts to clear space or anything, and there's a countdown timer that doesn't go. anyone else have this problem? does it say anywhere exactly how much space is needed?

Yeah, had the same problem myself on PS4, fixed it by turning the PS4 all the way off (and ignoring the prompt telling me not to turn it off). It's counting down as we speak.

You could also try deleting the game and reinstalling it (I did that too, but it didn't work until I reset the PS4 fully), but back up your save just incase.

Just got MGS V (PS4). My experience so far....

Got to Title Screen and hit start. Screen went black and "3 days after wakening" shows up on screen and that's it. Tried to close the application and it sat there for about 5 minutes thinking about closing it. Finally it went back to the black screen with "3 days after wakening" and then I couldn't do anything at all. Had to hold power button for awhile for it to finally shut off. Couldn't eject the disc either.

Great start.

I closed the application and then hard reset the console. That did the trick.