Like you both said we are a bit picky as we would like to live in this first buy but we are gradually moving away from that idea.

My ultimate question is this...Do I knock on their doors on the day of closing and present them with the new lease showing a $300/mo rental increase or do I gradually step it up?

Do the thing that's appropriate for your level of experience, do the thing that you're likely to succeed at first, and then gradually move up to slightly more and more advanced techniques... but, to quote South Park: if you try to ski a double black diamond without first mastering the green circles, then the blue squares, and then the black diamonds, "you're gunna have a bad tiiiiime". 

The National Bank Acts of the 1860’s kick-started this gradual change.

You'll start with a few people and gradually your meeting can grow.

I’m sure this could gradually be raised but would take some time. 

I know I will also need to talk to the tenants to see if they are actually paying these amounts, plus do a lot of other due diligence too.I believe this could be a good opportunity to buy them when they are not anywhere near market rent, and also not fully-rented out (3 vacancies out of 15 units), and then get them rented out and also move gradually to market rent.  

hahahaI own a few rentals out of town, but want to buy some within driving distance to gradually get a hang of property management side.Also want to develop a network of friends who speak Real estate :) , since I have none in my immediate network.

Seattle has been starting to gradually change tactics away from the most extreme permissive policies it was trying - basically let homeless do whatever they want whereever they want and try to tax amazon to continue acommodating it) though it mostly isn't publicly announced. 

Would you support such a change to tax policy if it happened gradually over time?