In general, structural steels produced earlier than the 1940's did not have to control sulfur or phosphorus. They only had to meet minimum tensile strength requirements. Another property the early steels didn't have to contend with is notch toughness.
A36 steel was developed in WWII to improve weldability and to bypass government fixed prices. It was new, improved, and was not included in the pricing schedules published by the War Department.
The suggestion that you limit the filler metals to the low hydrogen type is good advice. The other piece of advice I would offer is to take a sample and have a chemical analysis performed. The cost of obtaining the sample will be more that the actual chemical test, but well worth the effort. I would also suggest that you compare the various electrodes offered by the different manufacturers. Many manufacturers make more than one type of E7018 electrode. Likewise compare flux cored electrodes if you decide upon using the FCAW process. Select a filler metal with a manganese content that is at least ten times the sulfur content of the steel you are trying to weld. Use the low hydrogen electrode such as E7018-H4 or use a second generation flux cored electrode that will meet the low hydrogen requirements (not all flux cored electrode are created equal). The low hydrogen filler metal is necessary because most early steels had "higher" carbon content than most modern construction steels. Also, the chemical analysis will be useful in determining the minimum preheat temperature. I prefer to use the "Alternative Methods for Determining Preheat" found in Annex XI of AWS D1.1-2002 (for example). The details are in paragraph X16.2.2 and Tables XI-1 and XI-2.
The sulfur and phosphorus can lead to hot cracking. The higher carbon content can result in delayed cold cracking. The higher manganese will help mitigate the problems associated with sulfur. The high preheat and low hydrogen electrodes (properly stored on the job site at 250 degrees F) will minimize the delayed cold cracking problems associated with the higher carbon content often associated with early steels.
The last bit of advice I would offer is to have an AWS Senior CWI watch over the welding to provide a level of assurance the work is performed in accordance with a written welding procedure specification.
Ok, let this be the last bit of advice. Wait at least 48 hours to have the welds inspected using the magnetic particle test method if the welds are fillet welds or the ultrasonic test method if the welds involve complete penetration groove welds. The NDT technician should be certified by ASNT as either ACCP Level II or ACCP Level III. The reasoning is that the ACCP certification involves third party certification rather than only employer certification as is the case with NDT certification to SNT-TC-1A or CP-189.
Best regards - Al