As a Realtor, you have access to the MLS and insight that an investor might not have.

The easiest method is obviously using an agent as they have access to this information quickly.

These associations are incredibly valuable for education, advice, access to legal forms,  screening services, networking,  etc.If there is not already a tenant in place, be sure you understand how to properly and legally screen.   

I have access to contractors and handymen. 

Additionally, if the machines are damaged, you know who is accountable.If you are compelled to have a common laundry room then you need to explore access restrictions (keyed or keycode) and, possibly, surveillance.  

I'd like to hook up with an investor-friendly local lender or mortgage broker to see what kind of options or products I might have access to.

I am not super clear on what the best method to gain access to the equity in my house.

I think it's to gain access to their annual meeting.

I simply say "if we decide to work together, you get access to my entire rolodex, shall we start the process"?

You could just put in regular machines and not give your tenants access...of course, they won't be thrilled the first time they run into you with a basket of clean cloths under your arm.