That'll be on you to decide. Personally, for the athletics check, I'd probably do a DC 14 or 15 for plate and chainmail, and 12 for leather and cloth. Now, a quarter mile is a long way to straight up swim, especially if you don't have an extensive background in swimming, so I'd go with a DC 13 or 14 for everyone on the constitution check. I'd probably also give a level of exhaustion to anyone who makes it across.

Which brings up the next point. How do you handle failures? These aren't easy roles to make, depending on your party's level. If they don't come up with something creative to mitigate their efforts, a few failures are likely to happen. Now, the Suffocation rules say a player can last 1+ con mod minutes while holding their breath, then they start taking damage and last con mod number of rounds before they hit 0 HP. Now, I've always interpreted this as the number of minutes for a creature who isn't exerting themselves. Don't believe me? Go try running down the street while holding your breath. So in this situation, I'd rule they get 1+con mod number of tries before they start drowning, and figure out some sort of penalty to prevent the failed attempts from just becoming super advantage. Maybe give Xd6 points of damage per consecutive failure, where x is the number of consecutive failure. Basically you need something to impose a penalty for failure and to raise the stakes, but can't be so severe that the player might as well die right away.