Best way to upgrade a lenovo H50

Solution
You could toss in a better PSU and upgrade your GPU, however it's an old platform and not a very good CPU so you might wanna consider a full system upgrade looking at new mobo, ram and cpu.
Your upgrade options from the latest kit that's available will be much greater with whole new system.

Upgrading your current system within the limits of what an OEM motherboard supports would in my opinion represent a waste of money that could have been better spent by putting it towards a new system.