Sqatters Moved in and Don't Have to Leave

[Nia C.]

In short, I bought a property on a Friday. Less than a week later, people had broke in through my back door, changed the front door lock, and moved in. And they do not have to leave. They produced a lease and receipt for payment of 1st month and security. They claim that they saw the property on Craigslist. 

All Lies.

The people on the lease were found guilty of illegally possessing a property less than a year ago. They also have a rap sheet that includes breaking and entering.

What steps can I take to reduce the chances of 

   a. Someone breaking into a recently purchased property and then moving in.

   b. Someone being able to stay in the property at the point I discover they're there. 

c. Getting these people out of property. Is filing for wronful detainer in District Court the only way?