you could also consider the FX 4170 if you up the budget for about 8-13$ according to this month's budget gaming cpu recommendation in the Tom's Hardware monthlyhttp://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-3.html
"But the FX-4170 comes with a much higher 4.2 GHz base clock, and consequently offers compelling performance out-of-the-box. With a price tag recently lowered to $120"
As the FX 4100 is only 3.6GHz base and turbo core @3.8 GHz as compared to the 4.2 base and 4.3GHz turbo on the FX-4170.
Just a suggestion or you can wait and watch for the FX vishera CPUs
Also the 3870k APU requires the FM1 CPU socket and the other FX series requires the AM3+ socket so have you bought the motherboard already or you getting a buying decision on the platform, Personally I would recommend to go by the AM3+ route and get a Vishera CPU with better IPC and better clocks in a couple of months or so.