$800 PC build need advice. To upgrade or buy a new one?

[Zukane]

I'm torn between getting a new computer or just upgrading this old one. I want a computer that can handle 1080 ultra settings on modern games (Not really a fan of 4k gaming), be able to stream my games without lagging and probably record at the same time so I can edit them out later. I also need it to be able to make games from Unity or Unreal Engine. Currently this is my computer specs.

Current Build
CPU: Intel Core i3-2100 @ 3.10GHz
Motherboard: Gigabyte H61M-S2V-B3
Memory: 6GB Ram (Don't know what model)
Storage: ST31000524AS ATA
Video Card: NVIDIA GeForce GTX 650 Ti
Case: RAIDMAX AEOLUS ATX-818WB Black Steel / Plastic ATX Mid Tower Computer Case
Power Supply: (Don't know what kind of power supply I have, but I think I'll replace it anyway.)

and here is the build that I want to make.

Future Build
CPU: Intel Core i5-7500 @ 3.40GHz
Motherboard: Gigabyte GA-B250M-DS3H (Is there a cheaper one that works for this build?)
Memory: (Need suggestion on a 16GB ram)
Storage: Seagate BarraCuda 1TB HDD
Storage: Toshiba OCZ TL100 120GB SSD
Video Card: Gigabyte GTX 1060 Windforce 6GB
Case: Corsair Carbide Spec 01
Power Supply: EVGA 600 BQ

So should I upgrade or just buy a new one? I am sure that I have to replace both CPU,GPU, and Motherboard but for the casing I am wondering if the old one will work. Do you guys think it will fit right in? Also for my storage do I need to replace my old one or keep it and just buy the SSD? I'll be using air cooling. Any suggestions?

And if I am to upgrade, what should I get first?

 

[CountMike]

You might not need a new case but that's about it, everything else is a new build. Not much to upgrade old system to.

 

[EmmanuelEn]

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i7-7700 3.6GHz Quad-Core Processor ($294.99 @ SuperBiiz)
Motherboard: Gigabyte GA-B250M-DS3H Micro ATX LGA1151 Motherboard ($68.39 @ OutletPC)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2400 Memory ($101.99 @ Newegg)
Storage: Sandisk SSD PLUS 120GB 2.5" Solid State Drive ($49.99 @ Amazon)
Video Card: Gigabyte GeForce GTX 1060 6GB 6GB WINDFORCE OC 6G Video Card ($254.89 @ SuperBiiz)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($48.98 @ OutletPC)
Total: $819.23
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-30 05:57 EDT-0400

since you are going to edit ur gaming videos (video rendering) i7 would be the best choice for you.
i cant find OCZ TL100 on pcpp, but it has the same price.
ur old case would work with ur new build.

 

[Zukane]

Thanks for the reply guys. I'm going to keep the case and buy the rest. For the suggestion on Intel Core i7-7700 3.6GHz its still $100 more than the Intel Core i5-7500 @ 3.40GHz so I'll stick with that and bear with how long the rendering will be. For the memory thank you for suggesting G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2400 I'll buy that. Thank you again for your replies.