You can use either AC or DC to power the booster, within the specified voltage ranges, of course.
Here is what I use:
https://www.mouser.com/ProductDetail/709-ENP-360-24
It's a 13A fanless DC switching power supply. Runs nice and cool, and fits nicely in a stack with the other NCE gear. Under $80.
If you use a DC supply, there is also a simple mod you can make to the booster, which is to bypass the giant rectifier that the power input goes through. This cuts down dramatically on the heat generated in the booster itself, just in the process of rectifying the AC input.