Nice grabs!
I don't own any Hattori pots but they have a lovely quality to them that I appreciate, just they tend to be on the smaller sizes than I need
Tree selection for a pot is an interesting area to get into. The obvious one to do is a tree that has a colour (flower/ bark/ leaf) that is opposite the pot colour on the colour wheel that makes that colour pop more dramatically. This is done commonly with deciduous using a blue pot to make the red leaves even more attention grabbing
Another option is to use a tree that has subtle similarities to the pot colour, this enhances the tree while making the effect of the pot less noticable. This is what I did with the pot my Chinese elm was in for the show. I don't know for others but for me it kept forcing my eye back to the tree itself, like my eye didn't want to rest on looking at the pot at all
If you have a tree growing over a mossy rock I think the same effect could be achieved with this soft green colour nicely, or a tree with mature grey bark like an olive?
Think of it like a frame for a painting; gold leaf will make everyone look at your painting, but they may appreciate the gold more than the painting. A simple wooden frame won't grab attention, but keeps they eye on the painting itself. Same thing with pots and colour use
At the end of the day these are really final choice though, I use whatever pot I've got for whatever poor tree I'm repotting at the time and that's totally fine. Only thing I would 100% avoid is using the same colour pot as the feature you want to show off ie using a yellow pot to display a forsythia in flower