There is no such thing as a cheap psu.
A cheap PSU will be made of substandard components. It will not have safety and overload protections.
If it fails under load, it can destroy anything it is connected to.
It will deliver advertised power only at room temperatures, not at higher temperatures found when installed in a case.
The wattage will be delivered on the 3 and 5v rails, not on the 12v rails where modern parts
like the CPU and Graphics cards need it. What power is delivered may fluctuate and cause instability
issues that are hard to diagnose.
The fan will need to spin up higher to cool it, making it noisy.
A cheap PSU can become very expensive. Do not buy one.
Your psu need is gated by the graphics card.
You indicate a 7870 which is relatively power hungry, needing two 6 pin pcie power connectors.
That is typically available on a 500w psu.
I might suggest a tier 2 Seasonic S12II 520w unit for $30 after rebate:
https://www.newegg.com/Product/Product.aspx?Item=N82E16817151094
I might have suggested a more modern similarly performing GTX1050
FWIW
I will never again build without a ssd for the "C" drive. It makes everything you do much quicker.
120gb is minimum, it will hold the os and a handful of games.
But, many things default to the "C" drive.
When a SSD nears full, it will lose performance and endurance.
240gb is the recommended minimum.
If you can go 240gb, or 500gb you may never need a hard drive.
You can defer on the hard drive unless you need to store large files such as video's.
It is easy to add a hard drive later.
Samsung EVO is a good choice for performance and reliability.
Do some shopping; I found this 240gb Samsung 750 evo for $47.
https://raceprotax.com/products.php?product=Samsung-%252d-750-EVO-250GB-Internal-SATA-Solid-State-Drive-for-Laptops-%252d-Black