If you get an i5-4460 you would need a new motherboard. Any PCIe GPU will work in there, but what i would recommend for what you have vs what you are getting is different.
For the i5-4460 I would suggest you get a GTX 1060 6gb. Little overpowered for your current CPU but good for the i5.
Now based on what you can spend, the GTX 1050ti sounds about your limit.
You did not list what PSU you have, please provide that as you may need to replace it with a better quality unit. That will definitely blow your budget unfortunately.