Look for rust just above the front headlights. This is where the air intakes are located.
Look close in the trunk around the shock mounts and the trunk seams in that area.
Check battery tray for rust/acid.
Usual ~ check floorpans, rockers, front fenders behind the wheels.
As for parts ~ '57 stuff was everywhere 12 years ago when I did mine. Look into Kanter. Best bet is to do a search on
http://www.dogpile.com for the likes of *1957 Chevrolet Restore Parts*, and see what comes back.
Another option ~ go custom. I did this with another '57. Was easy to go to the local salvage and retro-fit late model interiors and such.
I lived in Jersey when I did mine, and was able to find a local supplier.
'57s are *very* popular cars. I don't think you'll have a big problem finding suppliers.
Good luck ~ and have fun!!