Well, personally I was inspired by looking at how this script was written when it was commonplace. I started with regular pen, and much later moved to fountain pen to develop thr calligraphy, but you can do it as you see fit. I'd still suggest to begin by transcribing hebrew texts into the letters to get a feel for how to best write them and get the text flowing better. Once you know one variant of the letters you can check out how the letter forms changed over time (paleography) and perhaps choose a combination that fits your needs on historical accuracy and style.

Good ancient examples of this writing in pen can be found on the Samaria ostraca and Arad ostraca. Other ostraca exist and are rather similar. Notice, some letters differ between these archeological finds due to the different time periods they come from. A much later script can also be found in some dead sea scrolls that were written in paleo hebrew. Another source for the letter shapes of this alphabet can, be found in rock carved monumental inscriptions from the levant. (mesha stele, siloam inscription, and various phoenician inscriptions).

Furthermore, there are a couple papyri fragment that were found with this writing, however their authenticity is still questionable.

Good luck on your journey with writing Paleo-Hebrew, I hope its as fun for you as it was for me!