Favorite pen: Lamy Safari fountain pen with EF nib, and Noodler's Black ink. I've been using this for many years and it's always reliable. The grip is comfortable and the construction feels solid (it's survived being dropped a few times with no real damage). It's reasonably priced and meant as a practical tool, not a fashion statement like some fountain pens. And Noodler's Black ink is waterproof and will write on the cheapest paper without problems. I've tried many other fountain pens and inks but I always come back to this combination because it's so trouble-free.
Favorite pencil: Rotring 500 0.5mm, with Pilot Neox 4B lead. I never much liked pencils before I found this lead. It's the softest I've found in 0.5mm, softer than most brands of 4B. It lets you write with very little pressure so it feels more like using a pen. The Rotring 500 has the same solid and reliable mechanism as the famous Rotring 600, but a plastic body so it's cheaper and lighter. But despite being a good pencil, I can't recommend it as strongly as the Lamy Safari because of one major flaw - it has no end cap. I reserve it for desktop use because the end pipe is completely unprotected and fragile.
I have no strong preferences for paper and IMO a good writing implement should work with any common paper.