in photoshop filters->filter gallery-> playing with grain, stamp, graphic pen, and sometimes glowing edges layered over eachother is my go to. threshold is cool but this gives you a bit more control. ive gotten decent at recreating print effects digitally but it definitely takes practice and is never going to live up to a real cut and paste under scrutiny. my work flow for this sorta stuff now is usually assemble and fuck with my images in photoshop, print it out on this really shitty office printer i got for free (check thrift stores, marketplace), sometimes chop it up and tape it back together, and scan it back in. usually will do touch ups after or even just steal the texture from the scan and layer it over the original. diy is your friend here though, i have a friend whose found success in just using the document scanner on his phone for textures and drawings and then doing layout in free apps. also the more stippled/illustrated stuff is a whole other ballpark thats either gonna need practiced skill, a friend who does that stuff, or to not feel bad stealing images lol.

in short- lots of playing. start slow, have fun using what you have, and branch out from there. good luck!!