Try this schematic on Nostalgia Air for the 62-555:
http://www.nostalgiaair.org/PagesByM...7/M0011597.pdf
The 93WG-555B model indicates it is a 1939 model made by Wells-Gardner for Montgomery Ward.
To power the set you could either make a power supply that will supply the 1.5V and 90V or you could use a couple of D cells in parallel for the filament supply and 10 9V batteries in series to get the 90V.
For the tubes make sure you are looking for the "G" suffix version and not the "GT" suffix version. The "G" version of these battery tubes will be the taller version. You could look through MDB Ventures site and find all the tubes you need. The ones labeled with TT for tall tubular should be what you need:
http://www.fourwater.com/stradio/stradio_sr1.htm#1A7-G
I have no affiliation with them but have purchased tubes from them a few times and have been very pleased with price, quality, and fast delivery.