What's the difference between a AM3, FM1 or FM2 AMD processor?
Those codes are sockets.
Overview of sockets here
FM1 socket info here
FM2 socket info here
AM3 socket info here
The socket type is just a way to keep track of the physical dimensions and electrical hookups of the CPU socket. Generally sockets will support one or more generations of CPU.
When thinking of upgrading your computer to something modern, you'll want the most modern CPU available, even if you don't end up buying a high-end one, because an up-to-date processor is always more future-proof than an older one.
The FM2 socket is the newest of the bunch, although the FM2+ socket (note the + sign) is the actual newest socket offered by AMD. Kaveri-generation AMD APUs run in FM2+ sockets.
Kaveri is a significant improvement both in terms of CPU and GPU performance over the older generations. Kaveri is actively in the process of being released to the general public, but an example model number of a Kaveri APU is "A8-7600".
Well I can't exactly rain down my past nostalgic experience like the 2 users the will enviably downvote or post comments not relating nor helping but I can be a judge of history.
Seeing how FM1 Front Bus Speed reaches a whopping 100 MH/z at highest clock, it won't do well and will certainly become a bottleneck real fast, so starting or running any process will slowly cap up the bandwidth on the FSB.
FM2 Allowing better architecture design for multiple processes, but still matching in contacts as of the FM1 but +1 contact, was basically FM2 just being a simple revision product. Along with FM2+ but now I am not one to bet on products from 2011. Definitely not obsolete for 3 years, I mean also inventing the technology to connect the north bridge was definitely some new push forward in processor development.
Oh an the AM3 Socket, ahh, I feel too nostalgic now, It reminds me of my first PC dream sound effects. But out of the way AM3 has about +40 contact points so better control, it is definitely common (to even meet the likes of me) but is more of what I like to call the 2012 era. I mean the FSB goes up 2x to 200 MH/z and allows a HyperTransport connection between the RAM and processor itself.
Honestly I don't know why are you buying these sockets, I would go for the LGA1100 myself but I can't help my love for Intel. But honestly speculating your using this for a Server of some sorts. Definitely go for AM3, case and point: Efficiency beats price tag, seeya.