Starting issues, will not restart after sitting

Car would not start, bought new battery and it started right up, let it run for a while then shut it off and restarted it appropriately five times with no problems. Let it sit for about an hour and tried to start it again and all it would do is one single click when I tried to start it. Let it sit for double digits hours went out it started right up. Drove it a few blocks came home shut it off waited a couple of seconds and tried to start it and all it did was the single click when I tried to start it different times. I am lost for a fix

Also, sometimes have to move gear shifter back and forth for it to engage so I can start it, but does not always work.