You still have utilities, HOA, replacements, sundries, pool cleaning, property management etc. 

(Search for the Due on Sale clause in a mortgage and you'll see plenty of threads and opinions on that but it is very common practice).I would focus 99% of your time on finding the right area and property, as well as team - agent, Property Manager (@Stephen Glover is a very good start on this one btw), banker, Contractor, etc.

Would you still be living in the area and managing it yourself?

I didn't raise the rent after the first year as suggested by my property manager, who doesn't raise the rent on his great tenants.

Chicago Property Management, Chicago Property Managers, Chicago Property Management Company | Straight Up Chicago Investor Podcast

I would use your VA benefits, like @Jason Wray said, but use it for rental property purchase that you can learn to manage.

@Kristi Tietz I've done some transactional funding for a few investors but I was branch manager for a mortgage broker in a previous life, so I'd overseen and fixed hundreds of closings. 

I had breakfast with another property manager, and we got to talking about the business. 

Create a well-structured investment plan that includes your standards, target markets, property types, financing techniques, exit strategies, and risk management plans.

It’s the simplest way to get a feel of what it is like to be a landlord without going through the hassle of managing rehab projects.