A 2001 German study found that a medium-firm pillow significantly improved sleep (the firmest was of no advantage). Bottom line: A pillow should support your head, not bury it.
Pillows also frequently contribute to allergies that impair breathing. The source of allergens can be the filling (down allergies are common) or dust mites. I highly recommend getting a nonallergenic foam pillow and a dust-mite-blocking protector. You should toss your pillow into the dryer every few months to kill dust mites and replace it every couple of years.
If you're in the market for a mattress, Consumer Reports found that people who spent 15 minutes testing a bed in the store—spending at least five minutes on each side, especially in their preferred sleeping position—were as satisfied as those who were allowed to take the beds home for a test sleep.