What's the best thing to upgrade in a PC with $150?

As most have said, upgrade your GPU now or wait until you have more money or there's nice sales. AMD cards offer great performance for the price, especially in 150-200 price range.
Don't listen to anyone telling you to upgrade your ram, because unless your gpu bottlenecks way before your ram will.

ssd

As most people have said already, definitely upgrade your graphics card. Everything else is pretty much fine, though after you can upgrade your SSD and possibly RAM if you have a larger budget.

HDD to SSD - Overall Performance Increase (bit less noticeable in games).
RAM to 8GB RAM - Will help with Multitasking activities, higher taxing programs and overall system performance.
Graphics Card - Will increase gaming performance.

This is if you have a decent motherboard that is. But if you really want to boost overall performance (games, system, applications), your best bet is to go with the SSD option. When ever someone moves to a SSD from a HDD, you will always hear them saying they would never go back to HDD.

For a SSD, I would recommend the Samsung 840 PRO 128GB. I did heaps of research on it and got myself one for about $140. It would be the best choice for a long term drive.

For the games you're playing right now, think of the most demanding one graphically. Can you run it at 1080p with no AA/AF at very good FPS? If the answer is yes, then I suggest that you save up another 70-100 USD for a better GPU. Definitely upgrade the GPU first though.

After upgrading the GPU, go for RAM. 8GB is going to be the sweet spot this year onward. Get a full 16GB if you can wait. That's going to give you a lot of headroom for multitasking. Today 8GB is the minimum if you want to multitask, like watching videos, download files, or do backups/transfers while you play windowed.