I saw some great graphs on popular mechanics website, I'd share the link but the pages are difficult to see on some devices.
Basically the graphs convinced me that a tungsten light source (with an 80B filter) would be a good choice.
Another type of light I'd recommend is electronic flash, if you can avoid short flash duration times. I use a box with an electronic flash that has a setting for flash duration 1/100th second which helps me minimize reciprocity law problems.
How much does the spectral quality of the light source matter when testing black and white film? It depends how much you are going to worry about the results that you get. I don't worry too much, but to explain what I mean, I'll tell a story.
I've tested 400 speed film with my electronic flash system and found the speed to be closer to 320, even when developed to ASA criteria. I've also tested Panatomic-X which has a rated speed of 32 and I find the speed to be closer to 50. Some of this remains a mystery, but as part of the test for faster film, I have a Kodak No.96 ND filter and another ND filter of unknown characteristics... which brings the light down enough for me to get the right densities to measure the film speed of 400 speed films. These two filters might alter the spectral characteristics of my light and it might be simply that Panatomic-X is more sensitive to a part of the spectrum of light that my filters transmit readily (for example Infrared light might pass easily through the ND filter).
If these little mysteries won't bother you, then really, any light source can be used.
An extreme example of the color of light problem is if you filtered the light with a color separation blue filter. It is well-known that the film exposed through the blue filter for color separation results in an image with less contrast, and the film needs to be developed longer to maintain color balance with the red and green filter negatives. So if you were to pick a very predominantly blue light, your tests for development time would be skewed significantly. You might conclude that your development times are longer than everyone else's.
So when you pick lights with different characteristics, you may get different test results... most of the time it won't be a dramatic issue. You obviously won't filter the light for pure blue. But you might end up with little mysteries like I found.