Top budget model under $100 for a B450 board.
Considering a mid-range setup within your budget, you might want a B450 model. Think about models like the 1600 or 2600 for your needs.
Last time I looked at the prices, it seems the Pro4 is likely the best option.
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MSI b450-A pro
For better savings on the CPU, consider a b450m d3sh.