nsk (the brand) do not ask for a 6001 because they will give you an open bearing (trust me, where do I work???) ask for a 6001LLUC3 (Sealed bothsides with higher radial clearence) also known as a 6001-2RSC3 or 6001VVC)
Spigot bearing= Pilot Bearing
Throwout bearing= release bearing
(Potato potato)
You got it, and no, clutch kits dont come with the pilot bearing