I was in the same situation as you a few months ago. I have an Acer slimline PC that I use as an HTPC. I wanted to do some light gaming on it, but the integrated graphics couldn't keep up. I started my search for a GPU. The one I needed had to be low profile with a single slot, since my slimline case wouldn't accommodate a full size card.
My other problem was my PSU. The one that came with my pc was only 220W. It's just not enough to run a discrete GPU. So I started to look for an upgrade. The only one I was able to find that would fit my slimline case was 300W. Again, it just wasn't enough power to run a good graphics card. Even if it was, it was really expensive anyway.
After some research, I found out that (while it's not very pretty) it is possible to run a standard ATX size PSU outside of the slimline case. I purchased a 430W Thermaltake for $40. I hooked up the cables as you normally would, but I kept the PSU itself beside the case, on the outside. I then found the most powerful GPU on the market (at the time) that could fit into my case. Again, it had to be low profile (skinny for slimline cases, and single slot). It was a Geforce GT 740. It came with a full size mounting bracket (not low profile) but you could remove the VGA connector and swap out the mounting bracket for a low profile one in about 30 seconds time. Since I was using HDMI, losing the VGA connector was no big deal for me. It has 2GB of GDDR5, which was a huge upgrade over my integrated graphics. I found it on Amazon for about $90.
Now, you don't have to do what I did. The point of my story is-your case, like mine, did not have a good solution for the PSU. Looking at your model of pc, it also looks like you will be limited on space, perhaps like I was. You have a few options. If you cannot find a higher wattage (low profile) PSU, you could run a standard one outside of your case, although it might not be pretty. While there aren't many small GPU's out there, there are a few. The GT 740 fit my budget and my performance goals.
Hope this helps.