Updating your graphic card is not enough to run recent games on 1080 Full HD, you need to upgrade your Cpu and RAM as well, look for a 4th gen i5 or higher and ram shouldn't be less than 8 GB, preferable 16GB
I doubt you'd be able to play at 1080p but what GPU are you working with currently? I would suggest a HD5770 at best(if you can find a second hand model ofc) Anything new will not be compatible with your platform.
P.S: You forgot to include the make and model of your PSU.
Updating your graphic card is not enough to run recent games on 1080 Full HD, you need to upgrade your Cpu and RAM as well, look for a 4th gen i5 or higher and ram shouldn't be less than 8 GB, preferable 16GB