According to MSI's website, that motherboard doesn't support 125 watt CPU's so you couldn't/shouldn't get an FX-8320 or FX-8350.
If you only want to spend <$150, an FX-6300 ($120) might be a good upgrade, but it depends what CPU you have now. If you already have something pretty good, then the FX-6300 may not be a worthwhile upgrade.
Are you mostly interested in gaming performance?
Replacing your motherboard is not that hard. Installing a CPU, thermal paste, and heatsink is more tricky and dangerous (risk of damaging CPU) than changing the motherboard.
You just take out your graphics card and any other cards, unplug the power cables and case header cables, and then there are 9 screws (I think) that hold the motherboard to the case. You should find some YouTube videos that will show you the process step by step.
Your current motherboard is micro-ATX size, so if you have a micro-ATX case, then you will have to get a micro-ATX motherboard. The 'normal size' is ATX, which might not fit in your case.
I would suggest getting something like an Intel i5-4570 and an appropriate socket LGA 1150 motherboard such as this one. That would run you about $300.
There are other options in between those two though.