Hawkeye has a decent right up but there are a few things that you might want to change up a bit:

Do not remove the pipes from the block connector at the firewall. If you do you will need a new set of O rings and spacers and you run the risk of cracking or breaking the plastic block that they snap into. Instead, simply remove the screw that secures the pipes to the bottom of the heater core itself. There are two simple O rings there that seal it, make sure you go back together with new ones.

On the whole coolant mess thing, take an empty coolant jug, the rectangular ones, not the round ones, and cut straight across the top so you remove the handle and poor spout, now cut about 4"off of the front and sides of it so all you have left is the flat back and the bottom which should be about a 4" deep rectangle to catch your coolant. When you undo the screw on the bottom that secures the pipes to the core make sure that you have the long flat back piece of your coolant catcher slid right up underneath the core/pipe connection. If you do it properly the coolant will flow right out and into your modified catcher and get not a drop on the carpet.

While I have yet to see them leak from the O rings, I have seen quite a few of the firewall block fittings crack and break. They are so notorious for it that any time I go in to replace heater hoses I always forewarn my customers that they may be buying a block if it goes bad.

Mark

You've already got the most important thing covered, you bought a Behr/factory replacement part.

Mark