Here's a $550 computer that might be able to play AH3 at 60 fps as long as the environment slider is at none.
From superbiiz.com (their "system builder" area, where you can select all the individual items). They build it for you, install the OS, test it, and ship it to you, with a 1-year warranty:
Mid Tower Case 1 Thermaltake Versa H21 CA-1B2-00M1NN-00 No Power Supply ATX Mid Tower (Black)
Motherboard 1 ASRock H97M ANNIVERSARY LGA1150/ Intel H97/ DDR3/ SATA3&USB3.0/ A&GbE/ MicroATX Motherboard
CPU 1 Intel Core i3-4160 Haswell Processor 3.6GHz 5.0GT/s 3MB LGA 1150 CPU, Retail
DDR3-1600 Memory 2 Kingston KVR16N11S8/4 DDR3-1600 4GB/512Mx64 CL11 Memory
Power Supply 1 Seasonic S12 II Bronze 520W 80Plus Power Supply
Hard Disk Drive 1 Seagate ST500DM002 500GB 7200RPM SATA3/SATA 6.0 GB/s 16MB Hard Drive (3.5 inch)
Operating System 1 Microsoft Windows 10 Home Operating System 64-bit English (1-Pack), OEM
total cost $438
Then add a $109 Zotac GTX 750 Ti from Newegg.com
total cost $547
By way of comparison, I have a Dell Vostro with an i5-2400 (3.1 GHz), 6 GB RAM, and a GTX 750 Ti, and I get 60 fps with defaults except for environment slider at none.
