Spritley, Phoenix canariensis likes a fast-draining compost, but it's not really very fussy. I am unfamiliar with the other plants you asked about. Do they have other names?

Chusan is Trachycarpus fortunei, Tug - this is the hardiest palm for Britain, but even so, needs shelter in colder areas. Grows in fairly ordinary garden soil. As for Phoenix canariensis, better in a pot - they're not frost hardy, so you can move it to shelter for the winter. I'd use John Innes No. 2.

Thanks, Bamboo! I'm still learning.
Spritley, I'm afraid that I just assumed that you would be putting the Phoenix in a pot--I should have been more specific. In light of Bamboo's comment, is a "european" maybe a Mediterranean Fan Palm?