THAT question has been asked so many times and 20 pages of discussion later, no clear winners.... here's my answer though.
Film developer: D-76 (works with every film, every photographer has used it, and highly available)
Paper developer: Dektol (same as above)
There are two different types of fixers. Regular fixer and Rapid Fixer. As the name implies, the latter works much faster. Also, there is something called "hardener" mixed into many fixers. This component makes (supposed to make) the delicate emulsion of film and paper more durable. Some says it isn't necessary. But it also makes washing time much longer.
I use Ilford Rapid Fixer which is both rapid and hardener free for both film and paper.
In the past, I used Kodak professional fixer for both and just washed longer.
Only thing with fixer is, fix long enough but not overly long and wash sufficiently long time.
Either one or different one will work just fine.
Now, 865 different opinions will follow mine. Stand-by....