Your existing CPU/setup will give us a better idea - if you're still on a Haswell platform (for example), then an i7-4770/K might be the 'best' CPU in budget.
Comparing pre-Skylake/Kabylake Pentiums vs something like a G4560 is not really fair. Pentiums have come quite a way.
That being said, I'm not sure how you're factoring a budget for just the CPU?
Either way, you're looking at a new motherboard too*.... and potentially RAM, so I'd recommend a budget for CPU+Mobo+RAM and go from there.
*Unless you're on Skylake currently, in which case I wouldn't recommend less than an i5..... but you'll consider Ryzen too, so that would necessitate a new board.....