A high shutterspeed isn't really necessary, because the flash will freeze the action.
Going with a high ISO is the way to get the background as well. But, using an umbrella will loose a lot of light, depending on the power you've got, maybe it is better without modifier.
But, if you don't mind me asking, is there a special requirement why you want to have everything frozen? It makes for a less dynamic picture. Just my opinion. I would typically drag the shutter (longish shutterspeed) with lower ISO, but long enough shutterspeed to give the background some definition. I'd still use flash to define the subject, perhaps on 2nd curtain (it flashes at the end of the exposure).
While not a great picture, this is an example of what i mean.