What Gpu would fit emachines EL1360-EW10P?

Id this what your PC looks like front and back?
KJdhkZ2.jpg


And is this what it looks like inside?
r3HCXLe.jpg
 
Then you are going to be severely limited due to 1) your small PSU, 2) the placement of the PCIe x16 slot. It is right next to the case wall making it impossible to use anything other than a slender single slot card. And 3) the slimline case will require a low profile gfx card. Before I recommend a safe card (for gaming?), open your case side panel and read the PSU's nameplate. What is the rating for the +12V rail?
 


Example please? But This is what I think it is : 14A Max
 


These are the important specs for adding a discrete gfx card:
4z102Sr.jpg

Is this your PSU?
 


That's it all right
 
OK. Bummer. Not much PSU there to run a gfx card. But you can use something in the AMD R7-240, Nvidia GT 730/740 range without problem. I was looking at Newegg Canada (it's the only place in Canada I'm familiar with) and found they don't have a big selection of...
Low Profile, Single slot cards that will work well with your limitations. I found these:
http://www.newegg.ca/Product/ProductList.aspx?Submit=ENE&N=100007708%20600286742%20600007855%20600007856%20600007852%20600038363%20600038364%20600473872%20600519936%20600515071&IsNodeId=1&name=GeForce%20GT%20740

I'm going to say that the Diamond R7-240 would probably be the safest bet. It is narrow enough to fit the limited space between slot and case side. It is only a 31W card. It comes with low profile brackets to swap out.
The other cards have a bit too much width even being single slot. The fanless Zotac GT 730 would be another good choice, but I'm afraid it might get too hot closed up in the tiny case next to the side panel with no where for the heat to go.
What processor you have in that PC?
What resolution is your monitor?
 


Amd E-450
1366x768
 


I don't really play much games lol, that's why I'm saving up xD for a new one. Plus I got this computer years ago and I didn't know about custom pc's until a year later xD