Using a 3D pen I printed a small box. However, I was doing it on plain paper and of course the paper didn't come off the plastic very well. It didn't matter for that specific case, but if I want to print something else, which non-sticky surface would you recommend? Is there any way to use transparent surface (so that I can put a paper with picture as a guide under it)?
You could use a piece of glass, that's what most people using 3D printers have as a build surface. An easy source of glass for pen use would be a picture frame but the edges are likely sharp so be careful. Acrylic would also work and is easily obtained in small pieces from places like Lowes/Home Depot, I used Acrylic for some time on my Kossel. The plastic can stick to Acrylic very well but I had no issues using it with my printer, just test it out and see what process works if you go that route.
You might want to experiment using Kapton tape. Although it's yellow-coloured, it is transparent and provides a good surface for hit-bed adhesion. You should be able to remove it from your print by flexing it.
Attaching it to your paper sheet is a one-way process, but you can use guide marks on the paper below.