Flying standby really necessitates using a “creative” carry-on bag that you can keep with you at all times with compartments and pockets for all the things you might need.
My favorite standby bag is made by Samsonite Silhouette Softside Carry-on and is the biggest that United airlines will allow. It rivals the size that the flight crew often carries. It has a compressible cube built in and a separate outer compartment for your toiletries.
The dimensions are 23in H x 15.5in L x 10.5in W and weighs 8.2lbs. It is expandable as well for those purchases that you want to bring home! The bag fits snugly on a 737 and really snug on the smaller planes (unexpanded!).