My plan is to purchase a property with a hard money loan, renovate and then refinance with a traditional bank.

Depending on your current overall tax situation, you might want to extract some of the equity (to gain some tax advantages) and redeploy it somewhere better (if you can do that) - then you should look into an asset based LOC or cash out refinance loan.  

or try to buy cash and then refinance?    

Then refinance and pull the money pay the HML back. 

We went with an FHA loan and are doing a house hack which left cash on the table to do the needed renovations so we could refinance our capital out of the property next year and move onto something else.

I have no mortgage and I want cash out refinance. 

You use it to fix the house, make it habitable, put in tenants to get income, then refinance with better terms.You could also look at getting a personal loan.

I also purchased this as first time buyer through FHA so I think I would need to refinance to rent it out and don't know what other considerations about buying another house I would need to think about and any information that would help would be greatly appreciated.

Pay cash and don't refinance.

Would it be worth it to make a profit if you have a bigger Refinance loan payment and lower cash flow?