For Faux Calligraphy you can use any type of pen or pencil or even a brush pen. You can use any marker, it just needs to have a tip that can do narrow lines as well as broad lines.
If you've followed my Instagram feed you've seen me use several different brand markers and pens in the past. Of the different pens I've used, my go to has to be the Faber-Castell Pitt pen. I like these so much, the colors are fun (there are so many to pick from), and these can be used for both faux calligraphy and in for brush pen calligraphy when you're ready.
This set included here is the Primary pitt pen set, This set includes 4 beautiful colors: Light Green, Middle Purple Pink, Cobalt Green, Orange Glaze.