I did a similar job for myself a while back on an old Southbend, it took the best part of 30 months so good luck!
The maximum safe speed will depend on several factors but mainly on the stiffness of the design as well as on the way the lubrication is provided for the lathe’s mandrel and probably a plain bearing headstock.
There were an awful lot of machines of this type produced 100 years ago and the quality varied hugely. Those intended for more serious use usually have a reservoir cast into the headstock with a felt wiper contacting the mandrel. The budget end of the market might be as cheap and cheerful as a “small-hole-and-oil-can-drip-a-drop-when-you-remember” job.
I mention this because one limit of top speed is the efficiency of the lubrication but as stated probably the greater limit is the stiffness of the lathe itself.
All that said I organised my lathe for a top speed of 1,200 RPM. The machine is of slightly later manufacture and a fairly stiff design but I’d say that was as fast as I’d want to push it.
For a machine of this age I’d not go much over 1,000 RPM. To calculate a speed is simple enough, you select the final speed, you have the motor speed so the required ratio is just a matter of driver over driven, (pulley diameters that is). It is desirable to have a selection of speeds and I would suggest a geometric set of ratios but remember that as the belt length is fixed the pairs of pulleys must be matched.
The second shaft you mention sounds like what is known as a “back-gear” and if so is there to provide a set of lower speeds in conjunction with the belt speeds. When it is assembled it should be possible to engage and disengage the second shaft. Thus the drive either goes directly to the mandrel or from the belt through the gears and back to the mandrel.
These observations are probably already too long for this forum so if I can be of further assistance please feel free to contact me.
By the way I started my toolmaking apprenticeship in 1956 so I do know what I am talking about… Just pass me Zimmer frame over!