I am pretty new to Premiere, and was editing some of my 4K footage and noticed pretty bad lag. After some research I discovered proxies, set some up, and they were still slow. I did some more research, found a recommended proxy preset, and tried that. Playback is still choppy.
My system has an Intel i7 6700k, 16GB RAM, and a GTX 1070 so I would assume it should be able to handle 960x540 videos. The preset I followed was found here:
What codec did you render to?
Do NOT use anything H264. If you are in ProRes or DNxHD at 1920 or lower, it should be fine.
If not, something else is the problem.
Start with a fresh project and just a few ProRes files imported, see if that works.