The exact budget and the question of whether you already got the RAM (and if yes, which one) will decide what's the best choice for you.
I'll list the options that come to mind by general pricing (which mostly equals to performance):
1. Intel Pentium G4560/4600/4620 + B250 motherboard
2. AMD Ryzen 3 1200 + B350 motherboard
3. AMD Ryzen 5 1500X + B350 motherboard
4. Intel Core i3-8350K + Z370 motherboard
5. AMD Ryzen 5 1600/1600X + B350 motherboard
6. Intel Core i5-8400/i5-8600K + Z370 motherboard
Edit: For your budget, options 3 through 5 are possible. Note that the Ryzen "X" and Intel "K" models come without stock coolers, so if you don't have one yet the only logical choice would be a R5 1600 build