I agree with Texases post, and emphasize especially USE A RAMP-TYPE LIFT.
If you put this on a pad lift and the rust is extensive, it could collapse on the lift and you could be hurt. Consider it unsafe for a pad lift until you can confirm otherwise.
Also PLEASE do NOT try to inspect the underside by putting this on jack stands and sliding under. If a jack stand punches through rotted metal while you’re under there, it could crush you.
IMHO, the only way you’re really going to be able to get into this project and end up with a good safe restoration in to gut the interior, pull the windows and trim, pull everything mechanical off, clean at and around the suspect areas with a media blaster (various types of media are available, including sand), and thoroughly check for rust and rot. Just welding a new floor in IMHO is unlikely to be safe. You really need to assess the condition from a structural standpoint.
As to the welding itself, there are a number of companys out there that make steel replacement panels and “clips” for these cars. IMHO the best way to get a safe car is when you find a rotted area you get a replacement section/clip/panel in steel, cut the old one out, and replace the whole area.
As a matter of fact, I’ll bet there are websites out there and books specifically devoted to restoring these cars. They were classic automobiles. There’s a whole “Z” subculture out there.