Today I broke the freewheel on my bike. It is a "Falcon" brand, 14 teeth on the small cog, 28 on the largest, 7 cogs, with less than 150 miles on it. Can someone please tell me if I am on the right track as far as replacing it?

1- Clamp Park tool FR-7 into a vise.
2- Put wheel/tire combo onto the tool.
3- Turn the wheel in the normal "loosen" direction really hard.

Eventually the freewheel and cogs unscrew. So far so good?

NEXT:
1- Buy this: http://www.ebay.com/itm/SHIMANO-7-SP...item43ab4b8015
2- Tap foot expectantly while I wait for it to arrive.
3- Lightly grease the threads on the hub
4- Very carefully, so as to avoid crossthreading, screw the new freewheel onto the hub.
5- Get it pretty tight with my fingers, BUT, it will actually self-tighten as I ride.
6- Put wheel on bike, ride a little.
7- Readjust everything on the rear derailer.

Does that cover it all?

What do I need to know about anything involving shifting, spacers, derailers, any of that?

Thanks so much for your assistance! I love doing my own work. Saving money is nice too.