I would do something light and airy to offset all the heavy wood and stone. And MCM in feeling too. I love any of the white light-as-air Nelson pendants.

Nelson pendant lighting at Design Within Reach

You could do singles, doubles, triples, all-the-same or mix-and-match. Here are some examples.

https://www.lampsplus.com/sfp/U7624/?cm_mmc=GOO-SH--NA--NA-_-U7624&sourceid=DFGPDU7624&gclid=Cj0KCQiAsvTxBRDkARIsAH4W_j8ggdZ4TvzbNPur7AJRNA8VTHpSlZKF9bgRYEZY216ZBfy7tylgDjoaAs7bEALw_wcB

maybe something linear

I found this photo of a somewhat similar space to yours, I think the chandelier on the back could fit in your space.

Private Residence - Wrightsville Beach, North Carolina. · More Info

before I answer that question, how is it to be hung and where is the power for it?

You are slighting limited by your beams, and the power source on how and where it hangs... there are always ways, like using track, swagging etc, but it would be good to know