Lite-on is the choice for Blu-ray drives that do scanning. Not necessary in my opinion. And Lite-on BD drives are getting scarce here in the US.
I have an older model LG and a Pioneer Blu-ray burner. Either brand should be fine
I prefer internal drives, and would recommend the Pioneer 209 series above most everything else due to Pioneer’s long history of good burning drives. That said, I have not used any of the external, USB 3 drives, like the LG BE14NU40.
Blu-ray burners will handle both single and double layer discs. Some have the ability to burn the triple layer BDXL discs also, but this is not universal, and the XL media is prohibitively expensive.