I suspect REI are likely to find that my proposed method of starting small but gradually increasing each month in a way that rent increases more than cover it will be far more manageable. 

If so, the seller financing method such as what Account Closed brings up a good idea about 1031s.There are other, more unique and creative solutions.

I'm exploring the real estate world and have been looking at a whole ton of different properties online and trying to scope out my first deal.

There are no secrets in real estate, we've been in this basic structure over a hundred years and there is nothing that is really new,  just a new twist to old methods, it's been done before.

Make sure they've done several deals in the area that you're exploring.  

I am young and don't have a lot to invest so I am particularly interested in methods for investing with low start up cash.

After that I hope to break into real estate somehow ( I've yet to decide exactly what I'll do—I'm in the early stages of education/exploration).

You will not find market cap rates and it is a less accurate method anyway. 

Is there a preferred method?  

It is a great place to explore and learn about REI, and take your time to discover what aspect most interests you.