Dont worry about that. The processor has nothing to do with the heatsink. the Athlon X2 +3600 has a low enough power consumption that it wont make a difference. The Athlon FX. Athlon64, and Athlon X2 all have the same form factor. That heatsink should fit, regardless. Hmm...

The radioshack website says that it is not compatible with Socket AM2, so you will probably have to buy another cooler

The Thermaltake site says it wont fit yet their packet does. I dont understand

With my socket type being an AM2 I assume all I need to do is find another heat sink that supports AM2? How would I avoid this happening again though? The packaging for this clearly states it supports AM2 and yet it wont fit the brackets AM2s come with. Any ideas on how to avoid this mistake in the future?

I know one that absolutely supports S AM2. This one
ARCTIC COOLING Freezer 64 Pro

Thats a great cooler.Even some Light overclockers use it.

Well, unless there is any specific cooling need, I would normally buy the retail version of the CPU rather than just OEM. The reail version will include fan which will fit most motherboards. I did see one AM2 with that connection, but most have a single holder either side rather than three (normally found on a 939). Here is an example:

< As you can see a single hole in this clip which will happily fit the socket on your motherboard.

Maplin > Akasa AMD AM2 Cooler

EDIT: Marked as Answered.