I currently have a primary residence home with about $225,000 in equity, and I have about $25,000 liquid, and a credit score in the mid 700s. 

If you are looking to invest into real estate, I have found this site to be incredibly helpful.There are a few self-contained guides that you can access here: https://www.biggerpockets.com/guidesI really like the alerts feature that can quickly guide you to current topics that might interest you: http://www.biggerpockets.com/alerts

I checked my score about 10 years ago and found a 620.

You can have different lenders pull your credit within a 30-45 day time frame without having a major impact on your credit score.

With that said, generally speaking you will need good credit history, and the score will vary drastically based on down payment and your debt-to-income ratio.

Am I correct in my understanding that shopping around and filling out several applications will only be reflected as one hit on my credit score?

I haven't read all the responses, but think of cap rates like bond yields, and then recall that there are people that buy bonds with negative interest rates because they can lock in their losses.In that environment, a 4.5% cap rate is incredible.

It was an incredible experience, but if I lost some money and gained experience, I still would have been thrilled I did it.After that, I aim for at least $20k on a deal.

Finding deals is incredibly tough right now, even compared to just a couple of years ago.

We are getting an Apple HQ over the next few years so you'll see continued job and wage growth.I also work with a handful of out-state-investors in both the Raleigh/Durham and Greensboro markets on purchasing rental properties with great success to take advantage of the aforementioned appreciation, great ROI on rental rates, and continued rent growth with the limited housing inventory and incredible demand.You can't go wrong buying in this market especially with the amount of capital you have and what I can only assume to be a strong DTI based on your original post.