And, even if you find a cheap program, they usually start going up in price as they develop and add more features.There are plenty of way to manage 1 to 3 units that don't require management SW.

Your budget should allow you plenty of options in the Red Bank area and similar neighborhoods. 

That being said, there are still plenty of ways to create cash flow here in Denver, and your opportunities will depend on what you can qualify from a lending standpoint.

You can spend 3 years studying nothing but real estate and I assure you there is still plenty you won't know.

You have plenty for all of that.

I went to Mexico on vacation and brought back a set of 4 tequila bottles which I put up on the bar as decoration until I wanted to drink them.

(They have plenty of handyman services)

Plenty of groups. meetup.com is your friend. 

We have about a million budget and are trying to decide between getting a tri or quadplex close to home for long term rentals and continue to self manage or invest in a short term vacation property up in the TN or NC mountains near a city with plenty of tourism (Gatlinburg, Asheville, etc.) what would you do and why??

Yes, there will be issues you will have to overcome that come with managing remotely, but PF/GB is a true vacation market that has plenty of resources to help you.