Hey @Dustin Hahn
Welcome to the community and real estate investing. Congratulations on thinking like this so young. This is an excellent way to reduce or eliminate your housing costs and truly treat your home as an investment. In spite of some conventional advice a house shouldn't be thought of an investment (unless your approaching things the way you are).
@Brandon Turner coined this strategy you're considering as house hacking. I've never personally done it but many here on this community have and hopefully can chime in on their specific experiences and lessons learned.
I'd like to address the general question of "Should I dump more into the equity to refinance for a down payment on the next one? Or should I minimize the monthly payment for more cash flow?" as this applies to whether you're living in the property or not. I think this depends on your goals.
1. If you want to keep this plex property long term after you move then I'd suggest keeping the cash flow and let your tenants' rents grow the equity gradually over time instead of dumping extra cash into the house to grow your equity faster. It doesn't make sense to put extra cash into equity and then turn around borrow that same money (with interest) as equity from the existing property to acquire another property. Just keep the cash and invest it when you have enough saved up and find a good deal. Cash gives you options and can be spent for whatever is needed. And when you only have one investment property cash is precious and fleeting as you'll probably find out sooner or later.
2. On the other hand if you plan to sell this property in the relative short term (2-3 years) for another larger/better property and have no better place for the extra cash then it isn't a bad idea to put some extra cash into the investment. Just know equity is illiquid and still subject to market swings. This equity can be used in a 1031 exchange for that next property and is tax advantaged at that point. But make sure you keep enough reserves for those unexpected expenses (they're coming I promise you... you don't know when and you don't know how much but oh boy are they coming).
So as with all questions the answer starts with .... it depends. Do you have a goal or strategy in place yet? I strongly suggest when you buy one deal that you are already thinking about the next 2-5 deals. Maybe not specifically but in concept at least. Set yourself up for the next move like you're playing chess.
Knight to e5
Having cash leaves your options open. So unless you have a specific plan I suggest hanging on to the cash. You can always pay down the principal later if you have the enviable problem of too much cash. Just consider your other options before you do that.
I'm in Little Rock and went to school in Fayetteville. From what I can tell your market is very strong for rentals and is enjoying steady and reasonable appreciation. Choose your moves wisely and you can do very well.
Best wishes and PM me if you have specific questions. Make sure to check out the local REIA and feel free to join us in Little Rock for our REIA meetings. We have several good national speakers planned for 2016.
check out www.carreia.com for details