I'd second everthing Chris has mentioned...
Spend at least the same amount on the protective clothing as on the saw as well. (on a new saw price, not second hand)
At least get trousers, gloves and eye protection - you won't even have time to react if a chainsaw decides to attack you!
Also a saw horse - DONT try and use your foot to hold the trunk!
Also, you'll need a log splitter (Maul) - not an axe, as they do different jobs.
Split the logs as soon as you cut them as they'll be easier to do than when they dry out.
Then leave them for a season at least before burning otherwise they'll deposit sap on the log burner liner and it'll run down the liner back onto the burner or into it.
Unless you're looking at logging quite a few trees and need the exercise it's probably cheaper to just buy them by the cubic metre from a seller.
... just a few tips I've learn't over the years