AM3 replaced the AM2 board. Initially, AMD released the AM3 variant which was backwards compatible with AM2 and AM2+ processors. The concept here is that AM3 can use DDR2 ram. Now, that being said,
it makes the most sense if you’re upgrading to a AM3 board (now you would use an AM3+ board), that you would want to use the more powerful processor and RAM. However, back in those days it was expensive to upgrade the RAM, processor and potentially other components at the same time.
These days, AM3+ boards and processors are somewhat inexpensive. Thus, if you want to build a good machine but avoid the newer Intel and Ryzen processors due to cost, AM3 / AM3+ is certainly an option. DDR3 RAM can still be expensive however; it seems all RAM is always somewhat expensive.
Best AM3+ processor: Likely the FX 8350 or 6300 series. The difference? The FX 8000 series line from AMD is 8 CPU’s, and the 6000 series is six core. There’s also a heat and wattage difference between the two. Some AMD enthusiasts report that in running the 8000 series, you need more powerful fans. Some builders will avoid the 8000 series so they don’t need to go with water cooling. It all depends on your budget and if you want to invest in things like water cooling etc.
If so, you may want to simply consider buying an AM4 board.
AMD AM3 vs. AM4 Socket & Motherboards
The difference between AM4 and AM3 (or the plus + versions) is that AM4 is the latest socket, which allows you to put a Ryzen chip in. You cannot put a Ryzen chip into an AM3 socket as they are not compatible, and there is a different number of pins in AM4 as well as a different configuration. AMD was smart in making AM2/3 compatible, but it does not happen with the AM4 board. Also, you need an AM4 board to run DDR4 ram, which has faster speeds (as did AM3 over AM2).