$100 budget

The OP didn't mention gaming so I still stand by the ssd as the best way to spend $100 to upgrade his PC. If he has the extra money then the ssd + graphics is a good idea but if not then I recommend ssd first, graphics later.

What PSU does your current system have? The R9 270 suggests a 500W PSU.

Durdy said:

If I bought a R9 270 what upgrades would I need to install it? A better motherboard?

Motherboard is not the problem but the PSU may be a problem as Strollin says.

The FX CPUs need an AM3+ socket. Does your mobo have that. And they also need a LOT of power - e.g. 125 Watt. Does your mobo supply that - in other words, what does your current CPU need.

Durdy,
It's always a good idea to list your builds spec's in your profile so we don't have to guess or play 20 questions.

Durdy said:

If I bought a R9 270 what upgrades would I need to install it? A better motherboard?

Your motherboard should be fine if you dont want hybrid crossfire then run the 270 which should be a decent price plus mantle

anyway SSD and video card should have you rolling for a while

Durdy said:

So I would just need to upgrade my PSU? Would I be able to just replace the APU? I might get a AMD FX CPU along with the R9.

Not unless you have more than $100 to spend decent upgrade at best $350

I have a better suggestion. Take that $100 dollars, put it into some savings, and save it. Add some more $100 dollars to it as you can and build it up. That way you can get something decent.