With limited savings, one of the cleaner entry points is an FHA or owner-occupied loan where you can house hack, and later depreciate the rental portion once you move out.

Two places I'd consider starting is (1) house hacking or (2) live in flip.

I can do conventional/FHA loans too, if you decide to house hack or get your own place.

Quote from @Aaron Zimmerman: Glen - are you in a position to house hack?

He then started house-hacking via room rentals. 

You can use conventional loans with as little as 3.5–5% down if you plan to live in one unit (house hacking).

What is your contractor saying it will take to rehab the place, has he walked it?

Best first step is always house hacking.

I love the idea of house hacking, and conceptually it seems like a great way to break into RE investing and build wealth.

There's absolutely nothing wrong with house hacking, doing a deal a year for a few years, building your network and relationships and using the resources you already have- like a VA loan, which can supercharge your start.