My handyman says these rents are still under market value and I can increase by about $650 and one unit is vacant so room to improve immediately.

Find one that needs a little love and do the improvements and either long term rent and refi or get it set up for short term rental and refi. 

I could also - instead of investing in a new property - use some of the $ to improve one of my properties - I have a bunch of it that's awaiting renovation and could then be rented out.

I know the bigger ones likely have quite a few relationships with bigger guys then me they feed deals to first so maybe call the younger guy on staff? 

I am a general contractor by trade and have thus far saved up money to buy all of my rental properties (and their necessary improvements) out of pocket.

The kitchens are all dated, the carpets are worn, and the landscaping needs some work.By making those improvements, we can increase the rents, which increases the income of the property and thus, the overall value.

Gives you roughly $450/ month to deal with turnover, management, capital improvements, etc. 

If the building is destined to be scraped off the lot to get highest and best use, I'd be very picky on midterm improvements. 

Improved all lighting and electrical in the house.

Welcome @Daniel Sanchez - my 3 non-negotiables would be to familiarize yourself with your credit score and the things you can do to improve it, figure out how much money you will need upfront so you can be prepared, and identify a target zone or zones in which to buy.