in all honesty i would be looking at the second hand market for an old i7 (like an i7 2600k).
ram and gpu's are very expensive at the moment, which makes it hard to a budget build at all.
assuming you don't need windows, mouse keyboard and monitor - this is as close as i could get. you could maybe get a case with a power supply already in it to lower the cost a bit.
PCPartPicker part list:
https://pcpartpicker.com/list/Pg3G3b
Price breakdown by merchant: https://pcpartpicker.com/list/Pg3G3b/by_merchant/
CPU: AMD - Ryzen 3 2200G 3.5GHz Quad-Core Processor ($99.00 @ Amazon)
Motherboard: MSI - B350 PC MATE ATX AM4 Motherboard ($55.98 @ Newegg)
Memory: G.Skill - Aegis 8GB (2 x 4GB) DDR4-2400 Memory ($88.99 @ Newegg)
Storage: Western Digital - RE4 1TB 3.5" 7200RPM Internal Hard Drive ($40.99 @ Amazon)
Case: Raidmax - Viper II ATX Mid Tower Case ($19.99 @ Newegg)
Power Supply: Corsair - VS 500W 80+ Certified ATX Power Supply ($19.99 @ Newegg)
Total: $324.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-02-14 23:44 EST-0500
-note that pc partpicker has flagged that the mobo might need a bios update but it might not.