I have a significant amount of cash saved up, but I would prefer to maintain my reserves for all the surprises that come with your first investment.

You just have to make sure you are confident in your analysis and have reserves for the investment to ensure you don’t put your primary residence at risk. 

When your borrowing from a "HELOC aka credit card its basically showing the bank that you do not have the "liquid reserves/cash" on hand to buy the property. 

Having used both personally for advertising and booking own reservations across the US and not knowing about Turnkey until you mentioned it, I am not sure what costs are but you might want to look at evolve which has been around a little bit longer. 

I think your better option would be to buy two properties as long as you have ample amount of reserves.

Ie: how many months in reserves, credit score minimums?

I'm hoping it doesn't meet reserve and it gives me more time to get things lined up. 

Whatever you do always have a reserve.

Then below that you can take out things like debt service, capex/reserves, etc giving you a "net cash flow." 

You can tweak the vacancy/maint/capex etc by setting up a reserve.