From Playstation Blog:

https://blog.us.playstation.com/2019/05/29/junes-free-ps-plus-games-are-borderlands-the-handsome-collection-and-sonic-mania/

Borderlands includes the first two games? If so that's awesome. I'll be sure to play it

No, it includes Borderlands 2, and Borderlands: The Pre-Sequel. Borderlands 1 is getting remastered later this year I think. 

I feel like I'm having the Mandela Effect, I could have sworn the collection was called "The Handsome Jack Collection" and not just "The Handsome Collection". Regardless, that is a decent PS Plus month.

I have such hate for Borderlands 2. It really was a uniquely terrible experience. Erased my save data ( and sold it ) as soon as i got the plat. Wish I still had that save data though. I could have used it to easily get the plats in in Borderlands 2 for both PS4 and Vita. It's a good month though. Most people don't despise that game like I do.

The remastered version is already out.

Weird that they didn't include the first game, but a prequel and the second game. Either way I'll play them. Have you? Which would you recommend I start with?

Borderlands 2 its a lot better then the prequel played it 100+ hours on both the X1 and 360 looks like I will play it a 100+ hours on the PS4 also looks like I will get PS Plus for at least a month starting in June.

I definitely approve this month! :)

Correct order is release order.

Handsome Jack was introduced as a character in BL2, then his story expanded upon with TPS, which is at least part of why the Handsome Collection doesn't include 1. I don't know why there isn't a collection that DOES, though.