$250 buys you aG4600, a lga1151 motherboard and 8gb of ddr4 ram.
You need 450-500w for a psu, Seasonic focus 550w is about $55 on sale.
Your choice on case, cheap is ok for a case, cheap is bad for a psu.
Update:
With the release of intel H310 motherboards, let me change a bit.
A H310 motherboard will be <$60.
https://www.newegg.com/Product/Product.aspx?Item=N82E16813157810
A G5400 processor will be $71.
https://www.newegg.com/Product/Product.aspx?Item=9SIA24G74W6067
Passmark ratings for the G5400 are not yet out.
But the G4600 clock was 3.6 and the G5400 clock is a bit better at 3.7
MMO games typically depend on the performance of the single master thread.
The single thread passmark rating of the G4600 is 2057 so I might expect the G5400 to be a tad better.
By comparison, the single thread rating of ryzen 1200 is 1728