I use old paper all the time. Anyone can make a nice print with new paper, but try to make a print sing when the stuff was dated to go in 1971, now that is fun.
For fixed grade paper, contact print a step wedge with no neg in the stage, no filters in the optical path, lens stopped down to f/8, or f/11 etc. Get the exposure time to put the area between all black and all white somewhere in the middle of the image of the wedge. The number of steps between just not quite white and cant tell between steps that are black AFTER THE PAPER IS DRY lets you compute the contrast range. If using a 1/2 stop step wedge (usually 20 steps) then number of steps x 0.15 gives you the density range. If 1/3 stop (30 steps) x0.1 per step.
The Kodak print projection scale, that gives the pie chart exposure test can even be pressed into service if you lack a formal linear step wedge; it will just use a bit more paper to test with it.
Make notes of the height, lens aperture, time, etc, and where the steps appear. If you do the same test with modern paper, then you can figure out the paper spped by conparing where the first non white happens on the old paper, relative to the modern paper. Then you can proof on your ordinary stuff, and then step to the special paper and know what the best exposure is likely to be on the first exposure.
The modern Ilford paper flyer has a little chart that shows how contrast range works relative to standard paper grades, and how filtration affects paper sped using the ilford filter series.
If you think you have a variable contrast paper, then you can expose a whole range of filters, from max yellow to max magentra with a dichroic head, or acetate filters, and map the current response of the paper. I regularly do this with all VC papers I use. I use strips of paper about 1" by 5", and write on the back the exposure and filtration with a sharpie marker before processing, and then use the best exposure found to keep the image still on the scale with max yellow and then also max magenta test strips exposed and processed first. Develop all for the same time, hopefully at some standard temperauture you usually use.