Lots of AM2+ can run AM3 CPU. These boards are often advertised as AM3 ready, and will only run DDR2. Often, you need an AM3 CPU to run 1066 DDR2 ram, with manual voltage settings in the bios. Otherwise they are limited to 800mhz. 1066 DDR2 is just 800mhz DDR2 that is rated to safely run faster.
AM3 ONLY boards, can come with either DDR2 or DDR3. As far as I know, DDR2 and DDR3 will not fit in the same slot. I have not personally heard of Mobos that can use both DDR2 or DDR3 on the same board, but there are mobos that come in both versions.
If cost is a concern, its perfectly fine to stick with DDR2. The performance difference is almost un-measurable.