I was wondering if I needed things like a copy of any insurance the seller may carry or proof of the tenant’s renters insurance, If that would be useful to keep on fIle.

If you send your go-to lender your most recent tax returns and mortgage statements for each property, he should be able to work it up in like 10 minutes (assuming your property taxes and homeowner's insurance haven't changed significantly since you did your taxes). 

FHA and the USDA loan have permanent mortgage insurance which is an added cost that does nothing for you, whereas conventional removes the mortgage insurance once you have 20% equity in the property so if you can do conventional that is generally preferred but if you can make the numbers work FHA can be a good option too. 

What system is everyone using to keep track of property information such as insurance premiums, maintenance records, age of the A/C, etc.

I know I sound like an insurance agent, probably because I am one. 

I think I'd like to have all my money back so I can get into another property, while my tenants pay down principal... and I'm budgeting for capex, maint/repair, vacancy, insurance, taxes, and management... but is the benefit of having nothing in the deal worth having almost no true cash flow?

1- Secure contract with purchase price and terms2- Send contract to title (search and insure)3- Draft note and mortgage (you'll need a lawyer to do this- less than $500 likely)3- Seller uses proceeds (your down payment) to pay-off  the lien (The title company will handle all this)4- Close the transaction5- Establish payments to sellerYou'll want to make sure there will not be a delay between the payoff of the 1st lien- executing the "lien release" and closing your transaction- will require coordination.

Make sure you have good insurance in case she burns down the house.

And that was before taxes/insurance, etc.

My holding costs include $500 rent per month, insurance, and taxes.