Folk Pop type music to Punk is probably about the hardest turn you could do so here some suggestions and punk music is not for everyone this is a long post sorry :(
Easiest stuff to get into:
MCR listen to any song on the black parade album I would recommend Dead! and Famous last words if you like this listen to the rest of their stuff its mostly good
The Offspring listen to Gone Away - 1997, way down the line and all I want they are probably their best songs but if you like any of those listen to the Ixnay on the hombre album its my favourite from them
Bad religion listen to Them and Us, 21st century Digital boy and I want to conquer the world if you like this then listen to their album no control
AJJ Since you like folk music this should be easier to get into but this one can be polarising due to the vocal and just being weird folk punk but id say listen to Brave as Noun, Rejoice, Gift of the Magi and Distance if you liked it listen to the entire people who eat people are the luckiest people in the world album
Jeff Rosenstock listen to Festival Song, to be a ghost and Scram if you like this listen to the entire Worry. Album
other stuff you might like: green day, PUP, Streetlight manifesto
Mediem level stuff to get into would be:
Misfits I would recommend listening to Where Eagles Dare, Last Caress and Bullet and their other hits but if your an album person listen to static age or the box set
Descendants I would listen to Hope, Coolidge and Subherban Home if you liked this listen to the whole milo goes to collage album
Jay Reatard this is personal favourite don't mind the name its just for shock value since that's what people called him when he went on stage. I would recommend My Shadow, It's so easy and I know a place if you liked it listen to blood visions
Hard stuff but try if you want to push yourself:
Bad brains listen to the self titled album
Minor threat listen to the self titled album
Chocking victim listen to 500 channels, Crack Rock Steady and Fucked Reality the album if you liked it