It would be liquid hydrogen, which is what we've used in rockets since before the Apollo program. In a liguid-fueled rocket, most of the weight comes from liquid oxygen. If your sub-orbital stage can get you to Mach 7+ and an altitude of a few dozen miles using atmospheric oxygen, you save a lot.
I think the plan is to use this as a booster for the final stage, or have it carry along some liquid oxygen for convential rocket thrust the rest of the way