I need to understand how to account for grant money I received for my business. I put the Vendor as the organization that gave me the grant, but what category do I use?

If you are sure you will not ever have to pay the grant back, you can record the deposit of grant funds directly into the other income account.  If there was a question on whether you would have to pay the grant back (PPP loans, for instance, for which you have to apply for forgiveness), you would want to record the original loan as a liability and then record the forgiveness as a journal entry to pay off the liability account with an other income account as suggested. 

Recording the initial deposit this way means that the amount you received, which you may or may not have to pay back, will show in your financials as a possible liability.  The notes in your financial statements could include specifics about that loan and the fact that it most likely will be forgiven, but until it definitely is, it needs to show as a liability.