How to install OS on new hdd w/no back ups available

Hello!

I have a 2012 Mac Mini and it started having issues about a month after Sierra was loaded on it. I installed High Sierra and the issues resolved, but then it started saying "memory corrupted" and after I started to trouble shoot the computer will not go past the apple logo screen. I replaced the RAM and it didn't resolve the issue.

My guess is the hard drive is bad.

Before I invest my time and more money into this, I am having trouble finding how to install the OS onto a new hdd. I have no backups available and I don't know anyone that has a Mac computer. All the info I'm coming across is stating I have to boot from the recovery partition or have another computer with at least Mountain Lion on it.

I bought this computer used, but I did have my Apple ID on it.

Any leads or info would be much appreciated!