I need a Build for my gaming rig (cousins')
budget - $500
Things to Exclude - HDD/Peripherals/Windows 10
Include - Wireless Network Card/SSD
Casing type - Small (Mini) to Mid Tower similar to Corsair - 270R ATX Mid Tower Case
Quite a challenge at that price point. But this should be a decent platform at a little over budget. Assuming you are US based.
PCPartPicker part list / Price breakdown by merchant
Yeah, this would be about as good as it can get unless OP can score some things that are open-box or pre-owned. Which might be worth looking into. Also just consider that the RAM and SSD are using the Newegg Business pricing so those items will be a bit more expensive unless OP has a business account.
What about if I stretch the budget to 600 dollars?
Upping budget to 600 means you get to improve one or two of following: CPU multi threaded 4/6 core, ram to 16GB or GPU 8gb version/rx580 8gb.
$700 is where you get a very decent all round 1080p system.
Out of interest, what games and monitor resolution will you need this system for? Above list is good starter for 1080p.
As Crofter mentioned, those would be things to upgrade if you increase your initial budget. Depending on your uses, I would personally try and upgrade the GPU a bit as I believe the R3 2200G is a great starter CPU and you shouldn't really require more than that if this is a first time build for 1080p gaming.
I would personally try and find a good used RX 580 and then spend the extra budget for 16GB of RAM.
I have a very light use on games. Not hard-core rather just normal games like they sims or csgo. Primarily uses my pc for streaming and maybe some programming
If you're wanting to stream, then I would probably say to try and get a bit more CPU. The R3 probably wouldn't handle streaming very well. If you're able to stretch the budget, try and go for the Ryzen 5 1600 since that is a 6 core / 12 thread CPU.