Do I have a build that would play Skyrim @ 60 fps?

Well awhile back I got the Windows 10 64-bit OS disc and it's not SSE it's the original Skyrim the 2011 version, thanks for that I didn't realize it was just 4gb of RAM. I am thinking of running on medium settings since I am accustomed to the very low end of gaming because this will be my first build in a very long time of constant 60 fps play on Skyrim.

I saw another build, though and was wondering can it run Skyrim at medium settings @ 1600x900 @ 60 fps?
https://pcpartpicker.com/list/psrXXH

Or should I just buy a prebuilt with an i5-7400, 1060 3gb at a lower price?
https://www.amazon.com/HP-Pavilion-580-023w-i5-7400-Graphics/dp/B077S27YLP/ref=pd_sbs_147_29?_encoding=UTF8&pd_rd_i=B077S27YLP&pd_rd_r=MV4JCN4MENH80ED9ZHZW&pd_rd_w=2ZR6d&pd_rd_wg=LhEW6&psc=1&refRID=MV4JCN4MENH80ED9ZHZW

Could you list parts please

EDIT: It says $742 not $642...well I DID say $600-800 but i'm looking for something like around $650 sorry guys that I mislead you =[

EDIT 2: Now it says $642 again. Glitchy

Final EDIT:
[PCPartPicker part list](https://pcpartpicker.com/list/6WXBQV) / [Price breakdown by merchant](https://pcpartpicker.com/list/6WXBQV/by_merchant/)

Type|Item|Price
:----|:----|:----
**CPU** | [AMD - Ryzen 3 1200 3.1GHz Quad-Core Processor](https://pcpartpicker.com/product/TX4NnQ/amd-ryzen-3-1300x-35ghz-quad-core-processor-yd1200bbaebox) | $109.00 @ Amazon
**CPU Cooler** | [ARCTIC - Freezer 7 Pro Rev.2 45.0 CFM Fluid Dynamic Bearing CPU Cooler](https://pcpartpicker.com/product/VRPfrH/arctic-cooling-cpu-cooler-freezer7prorev2) | $17.99 @ SuperBiiz
**Motherboard** | [MSI - B350 TOMAHAWK ATX AM4 Motherboard](https://pcpartpicker.com/product/Y4kwrH/msi-b350-tomahawk-atx-am4-motherboard-b350-tomahawk) | $65.98 @ Newegg
**Memory** | [Crucial - 8GB (1 x 8GB) DDR4-2400 Memory](https://pcpartpicker.com/product/N3yxFT/crucial-8gb-1-x-8gb-ddr4-2400-memory-ct8g4dfd824a) | $84.88 @ OutletPC
**Storage** | [ADATA - Premier Pro SP600 128GB 2.5" Solid State Drive](https://pcpartpicker.com/product/zc8Zxr/a-data-internal-hard-drive-asp600s3128gmc) | $47.99 @ Amazon
**Video Card** | [MSI - GeForce GTX 1050 Ti 4GB GAMING X 4G Video Card](https://pcpartpicker.com/product/H97CmG/msi-geforce-gtx-1050-ti-4gb-gaming-x-4g-video-card-gtx-1050-ti-gaming-x-4g) | $159.89 @ OutletPC
**Case** | [DIYPC - Solo-T1-R ATX Mid Tower Case](https://pcpartpicker.com/product/8ZL7YJ/diypc-case-solot1r) | $24.98 @ Newegg
**Power Supply** | [Corsair - CXM 550W 80+ Bronze Certified Semi-Modular ATX Power Supply](https://pcpartpicker.com/product/3hkwrH/corsair-power-supply-cp9020102na) | $51.99 @ Amazon
**Optical Drive** | [Lite-On - iHAS124-14 DVD/CD Writer](https://pcpartpicker.com/product/6fJwrH/lite-on-optical-drive-ihas12414) | $10.99 @ Newegg Marketplace
**Sound Card** | [Creative Labs - Audigy SE 24-bit 96 KHz Sound Card](https://pcpartpicker.com/product/f4zv6h/creative-labs-sound-card-30sb057000000) | $22.99 @ Newegg Marketplace
**Wireless Network Adapter** | [Edimax - EW-7811Un USB 2.0 802.11b/g/n Wi-Fi Adapter](https://pcpartpicker.com/product/hHdqqs/edimax-wireless-network-card-ew7811un) | $7.99 @ B&H
**Case Fan** | [Cooler Master - SickleFlow (Blue) 69.0 CFM 120mm Fan](https://pcpartpicker.com/product/sdZQzy/cooler-master-case-fan-r4l2r20acgp) | $6.69 @ OutletPC
**Monitor** | [Acer - K202HQL 19.5" 1600x900 60Hz Monitor](https://pcpartpicker.com/product/xTvRsY/acer-monitor-umiw3aa008) | $69.99 @ Amazon
| *Prices include shipping, taxes, rebates, and discounts* |
| Total (before mail-in rebates) | $726.35
| Mail-in rebates | -$45.00
| **Total** | **$681.35**
| Generated by [PCPartPicker](http://pcpartpicker.com) 2018-01-02 00:04 EST-0500 |

I have all the parts which come to $726 which is still a really great deal. Thanks guys for helping me figure out a build to play Skyrim on. Here's for hoping they release TES: 6 before 2050!