I vote for the used Fastback, if everything on it works as it should and it fits reasonably well. It's from a period when Schwinn tried to address two markets at the same time, independent bike dealers and big-box discount stores. This was one of their IBD bikes, quite nice. And 10-speed 105 (5600) is a solid workhorse of a drivetrain.
The Giordano Libero is not a 24" men's bike, it's a kids' bike with 24" wheels. That should close the debate right there, unless you happen to be shorter than 4'10". The Schwinn Phocus is another cheap bike made for big-box stores. It will be built, but not well. Figure on $70-80 to make it ready for your charity ride. Big-box stores don't service the bikes they sell. They give you store credit if it's inside 30 days and you have a receipt, and throw the bike into the crusher.
If anything is out of adjustment, though, don't hesitate to downgrade your offer and then have the bike tuned by a good bike shop. Fiddling with derailleur cables is not something a newbie should be doing days before a charity ride.