Grahpics card to support 1920x1080

[terry776]

Hi, I'm very new with hardware and I need help picking out a graphics card.
Currently my computer is a HP Pavilion P6000.

My monitor is a Benq XL240T 1920x1080 resolution and I need a graphics card that can support it. I play League Of Legends and my fps is constantly sitting at 10-18. Only problem is, is that my power supply is 250w. And I don't want to spend money on a card just for it to fry. Any suggestions that could let me play at 50fps+ and work with 250w psu? Thank you

 

[terry776]

Also some youtube videos, the quality is really really bad even though its set to 720/1080p is that also because of my card? I used to think it was the video itself but its been happening on a lot of videos so I'm not too sure.