Mrs. B - my hair also got even more curly after being on MTX for years. That stuff actually changes things at the DNA level... I hated that med.
Prednisone doesnt really make the hair fall out too much,as others have said, it usually causes hair to grow on your face, etc.
Arava makes my hair fall out some but not as bad as MTX did. I have been on Pred for 12plus years and I dont think it helps the hair much, but not much loss anyway. My hair is so trashed from all the meds.
For more info on pred, look on the major med sites or ask your doc. There is LOTS of info on it since its been around for so many decades.
Straight hair is all the rage these days, so I wouldnt get a perm myslef... as I already have curly hair. Its a pain sometimes. That is just me tho. I dont like the perm chemicals anyway.
best of luck.