Processor

Intel Core i3-4160 - $119
The Core i3-4160 is an unbeatable proposition at this price. It may be a dual-core chip, but features HyperThreading, so games see it as a quad-core chip. There are cheaper Pentium and Celeron-branded dual-core "Haswell" chips, including a new line of Pentium SKUs with 3 MB L3 cache, but those chips lack HyperThreading, and some games (eg: FarCry 4) have stability issues with them. Call it bad coding on the game developers' part, but some games just can't work properly without seeing at least 4 cores. One way to trick them into doing so is HyperThreading.

Based on the "Haswell" architecture, its per-core performance over AMD's "Piledriver" is high enough to make us recommend this chip over even the six-core FX-6300, which can be had at just $104. If we're trying to squeeze the most fps out of our games at $800, the i3-4160 remains the safer bet. This chip offers 3.60 GHz clock speeds without TurboBoost, which, along with the 3 MB L3 cache and HyperThreading, should lend it enough muscle for high-detail 1080p gaming.

Motherboard

GIGABYTE B85M-Gaming 3 - $59
GIGABYTE believes that its $59 micro-ATX motherboard based on the Intel B85 Express chipset has the chops to drive a gaming PC. The company went ahead and gave it its coveted G1 Gaming branding. We, however, picked this board over the plethora of $50-ish boards based on B85 or H81 chipsets not because of its marketing, but because:

• It's one of few boards at its price-point to offer Intel GbE LAN. Intel makes good onboard Ethernet solutions with rock-stable drivers, low CPU overhead, and better bandwidth yield.
• Onboard audio with ground-layer isolation (no electrical noise in your headset), electrolytic caps (more 'natural' sounding music), etc.
• PCI-Express gen 3.0 x16, something $50-ish boards based on the H81 chipset lack.

Memory

Mushkin Enhanced Stealth 996988S (2x 4 GB, DDR3L-1600) - $42
8 GB continues to be a sufficient amount of memory for gaming unless you want a great amount of future-proofing and do creative-productivity tasks. There are still very few games that can saturate 8 GB and even those that do aren't heavily impacted by 8 GB vs. 16 GB.

There are a ton of 2 x 4 GB kits for around $40-50, but we chose the Mushkin 996988S because it's one of the most recently launched kits, supports the modern DDR3L-1600 standard with a vDIMM voltage of 1.35V, and offers timings of 9-9-9-24. Other kits in its price-range suffer from imperfections in their command-rates, vDIMM voltage, timings, or price. A lower vDIMM will go easier on your motherboard's power distribution.

Having spent $119 on the CPU, $59 on the motherboard, and $42 on the memory, we burned through a quarter of our budget and are left with $580. There's still a long way to go.