Great advice regarding finding a used PC, and then plopping a 750ti or another GPU that doesn't require a PSU swap or PSU power connectors for an entry level computer to get into AH3 with. The aforementioned dual core Intel CPU PCs, or even early i7 8xx to say 920 and such can be found VERY cheap if you search through the local used online sales sites in your area.
kijiji.ca here in Canada, I've found dozens of such systems for a couple hundred bucks that work just fine, and for around 100 USD if you look for deals you can find a good GPU like a 750ti - I have a home theater PC that's an i7 920 that came with a 5770 originally that I've put a 750ti in I got for cheap, and have flown AH3 offline with it a bit, and it works great with the reflection turned to 1 or off, and some details turned down a bit. Maintaining 60fps at 1080p with textures and some stuff turned down is very possible.
The 1060 is great for the money, but requires a PCI E connector, which means with a budget used PC that you probably need to swap PSUs, and at that point it's getting close to the cost of just building a new budget PC is worth it IMO. The 750ti, or even the 950, both don't require a PCI E power connector, and usually a 350 to 400 PSU will get you by on either of those cards.