I would not recommend any CPU that will drop in your motherboard. That platform is dead and I would not put any money into it. The good news is moving up to a more modern CPU will really make a big difference. Streaming takes a lot of threads, so I would look at the AMD 1600. The 2600 is a better buy but will be a little bit more, so the 1600 will have to do.
Intel CPUs game better than AMD, but AMD will stream better then Intel. So AMD would be a logical choice. But you cant go wrong with the 8400 either.
PCPartPicker part list:
https://pcpartpicker.com/list/49NWTH
Price breakdown by merchant: https://pcpartpicker.com/list/49NWTH/by_merchant/
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor ($174.69 @ OutletPC)
Motherboard: ASRock - AB350M Pro4 Micro ATX AM4 Motherboard ($59.99 @ Newegg)
Memory: G.Skill - Ripjaws 4 Series 8GB (2 x 4GB) DDR4-3200 Memory ($102.99 @ Newegg)
Total: $337.67
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-04-25 17:26 EDT-0400
Here is the Intel:
PCPartPicker part list:
https://pcpartpicker.com/list/pgFkdX
Price breakdown by merchant: https://pcpartpicker.com/list/pgFkdX/by_merchant/
CPU: Intel - Core i5-8400 2.8GHz 6-Core Processor ($178.89 @ OutletPC)
Motherboard: Gigabyte - B360M DS3H Micro ATX LGA1151 Motherboard ($65.99 @ SuperBiiz)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2666 Memory ($83.99 @ Newegg)
Total: $328.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-04-25 17:28 EDT-0400