To follow up on what Koraks said, if you run a strip of paper through the developer, stop and fixing process, also put a strip ONLY through the fix - then you have something to compare the processed paper to, otherwise your developed strip may look perfectly fine.
You're probably aware you have graded paper, but I thought I'd mention it since I, too, started with a lot of old papers, some of which were graded, some were fibre based and I had NO idea because the previous owners had all removed the data sheets. Speaking of, I do have copies of some for older papers and can scan and post them here if they'd be of assistance. Anyway, regarding the graded paper, no filters required, so that can be a good thing when you're just starting out - one less variable to worry about.
I've actually had good luck with old Ilford papers as far as fog goes, however, a lot of them have suffered contrast loss - some far more severely than others.
Both fog and contrast can be dealt with to a certain degree chemically, although I've never tried the latter 'cure'. For fog, get your hands on some benzotriazole to pop in your developer. I've contributed to a thread here on Photrio with test strip photos and the dilutions I use (read the whole thing because I made a typo in the formula!). I'll find the link for that in a minute. You can also over expose and under develop a bit to bring up the blacks before the whites start fogging.
To up the contrast, I've no idea why I've never made my way around to it, but supposedly one can add a solution of Sodium Carbonate to make one's developer more active.
David Lyga here on Photrio has also detailed his 'Aged Fogged Film and Paper Rescue Remedy' - don't Google that, I'm pretty sure that's not how he entitled his thread. Anyway, search for his posts and he gives a very thorough description of how he deals with foggy paper.
I'll be back to add those links I mentioned....