I'm trying to build a budget PC system (around $600) and am wondering what the best CPU is for under $100. I have no preference for Intel or AMD, and am not looking for max performance, just the most bang for my buck.
Here is a build that includes the i3-2120 cpu and the total for thid comes to $597.92 and since I didn't know all of your details of what you need and don't need this is at this point just a guess. But you can look at it and see what you think and it's just an example of a build in your budget range that includes the 2120 cpu.
For BF3, i5 may be worth considering. For chess, that would depend on your patience. For most other stuff, it depends on how high your expectations of running future games are. If you are targeting games 1-2 years in the future, i3 could be good enough. If you want to stretch the PC for 3-5 years, i5 would be a safer bet.