So for example I'm very conservative and don't want any debt on them because I feel this hardens them in case of a severe recession.

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If your debt to income ratio is good, you can control a $700-800k asset with $50k.

You have used home equity lines of credit to purchase investment rentals and want to know the best way to pay down the HELOCs.Between the two properties you bought, after expenses, you have $250 a month positive cashflow to use.What I like to do is pay down some principal every month with my positive cashflow.I use my extra active income from real estate commissions helping other investors to pay down the principal even more which just frees up that credit for me to use again.I know I can refinance the HELOC debt before it changes to principal and interest as it is just interest only payments as yours are.One difference is the cashflow, I have greater positive cashflow and could make the principal and interest payment in the future with the extra cashflow I already enjoy.I always get HELOCs on my income properties as well after purchasing them to pull out as much of my downpayment as possible.

The majority of investments is a game of "race to the bottom" and "who holds the cheaper debt" card. 

If you focus on long-term holding for five to seven years, then using the above scenario on the house you are looking at, you will make significantly more on appreciation and debt service than cash flow. 

I am currently unmarried, no kids and recently out of residency with six figures in medical school debt.

For your scenario, you would be able to afford $8300 monthly mortgage assuming no debts. ($200K/12 months = $16k/ month of 50% = $8333.

Eliminate debt, establish a budget, and save.

could it service the debt on $1m?