Is this a good $450 gaming build

A few slight concerns:
1. Single channel ram has a noticeable performance decrease vs dual channel ( 1 stick vs 2 sticks)
2. That powersupply is cutting it really really close to what is barely passable. A bad/troublesome PSU can cause any number of hard to diagnose headaches, it's best to get a good quality one so you don't have to deal with problems you can't explain.

Here's what i'd do:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G4560 3.5GHz Dual-Core Processor ($59.99 @ SuperBiiz)
Motherboard: ASRock H110M-HDS Micro ATX LGA1151 Motherboard ($46.99 @ Newegg)
Memory: Avexir Core Series 8GB (2 x 4GB) DDR4-2400 Memory ($46.90 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.33 @ OutletPC)
Video Card: PowerColor Radeon RX 470 4GB Red Dragon Video Card ($158.98 @ Newegg)
Case: BitFenix Comrade ATX Mid Tower Case ($27.99 @ NCIX US)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($48.99 @ NCIX US)
Total: $439.17
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-06 14:45 EST-0500

Only problem with that buld is that H110m motherboard not shipping with a bios that supports the G4560.
We are still 2-4 months out from being able to safely assume that the motherboards will ship with upgarded BIOS.

Thus the only safe-bet right now would be to get a b250 motherboard.

You're right, I forgot about that, thankfully it's not that punishing to solve:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G4560 3.5GHz Dual-Core Processor ($59.99 @ SuperBiiz)
Motherboard: ASRock B250M-HDV Micro ATX LGA1151 Motherboard ($66.98 @ Newegg)
Memory: Avexir Core Series 8GB (2 x 4GB) DDR4-2400 Memory ($46.90 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.33 @ OutletPC)
Video Card: PowerColor Radeon RX 470 4GB Red Dragon Video Card ($158.98 @ Newegg)
Case: BitFenix Comrade ATX Mid Tower Case ($27.99 @ NCIX US)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($48.99 @ NCIX US)
Total: $459.16
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-06 16:14 EST-0500

The problem is MIR take months to come through and budget builds aren't about saving money in the end, they're about meeting a certain budget because that's how much cash they have on hand right now.

Any SATA HDD will work with any motherboard that have a spare SATA port for it. If you already have HDDs you can reuse then reuse them with my build, as that will give you the best price/performance.

Now if you want it to be ~$425 and you want it now:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G4560 3.5GHz Dual-Core Processor ($69.99 @ B&H)
Motherboard: ASRock B250M-HDV Micro ATX LGA1151 Motherboard ($66.98 @ Newegg)
Memory: Kingston FURY 8GB (1 x 8GB) DDR4-2400 Memory ($50.83 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: MSI Radeon RX 460 2GB Video Card ($99.99 @ Amazon)
Case: DIYPC Ranger-R4-R ATX Mid Tower Case ($25.98 @ Newegg)
Power Supply: Corsair CXM 450W 80+ Bronze Certified Semi-Modular ATX Power Supply ($32.99 @ Newegg)
Base Total, after promo code & shipping: $426.75
Mail-in Rebates: -$30.00
Total: $396.75
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-08 06:23 EST-0500

This will be a big downgrade from the prior build, but all those Avexir RAM, whether it's the 1x8GB Blue LED on my build or 2x4GB red LED on James build, come with a notice that they'll ship in 1-4 weeks and that G4560 are all sold out everywhere else but B&H (I think Amazon still have the G4560 but price it at G4600 level).

This Kingston (HyperX) Fury 8GB DDR4 2400 CL15 has the part number: HX424C15FB2/8. Do note the number 2 for when you have the budget for the 2nd stick as that denote the difference between the Single Rank module with the Dual Rank one; which will have an effect on compatibility if you pick the wrong one for a future upgrade. And no, at this performance level, you do not need to worry about dual-channel vs single-channel memory bandwidth. Either the CPU or the GPU will be the bottleneck long before memory bandwidth become an issue.

RX460, this is the main culprit for the downgrade performance. But why RX460 and not GTX1050?
1st> What everybody know. Better DX12 performance. DX12 has a greater effect on lower-end CPU so it's the better pick when paired with the Pentium.
2nd> What fewer people know. Because you can unlock an extra 8 TMUs and 128 Stream Processors with it (15% increase) if you'd be willing to overwrite the card BIOS. And the fact that you can increase its power limit to attain a bigger overclock on the card. Combine the two, you could get an increase of up to 27% performance over stock config.
Both of these have downsides however, (a) the custom BIOS file will make the card have compatibility issue with certain driver version. Do backup driver that work before updating to a newer one; (b) with increased power limit, you can overclock the card hard enough to make it draw ~100W from the PCIe slot (that's way higher than the spec for the slot: 65/75W), so don't go too crazy on those numbers unless you want a dead MB.

The case, on the other hand, is purely budget compromise.

CXM450: semi-modular, 37.4A@12V ~ 450W. S12II SS520-GB: non-modular, 40A@12V ~ 480W. But sale price ends for the CXM within 20 hours.