Brain freeze that I didn't mention the airport of departure. I updated the OP. I will be leaving from VIE and landing at AMS.
Would I need to go through immigration for an intra-Schengen flight? I've been to AMS a few times but I would need to read the signs to get me to where the shuttles pick up passengers.
I'm considering the Hampton by Hilton Amsterdam Airport. It's got a decent rate for HH members. I'm not staying at the Crowne Plaza Schiphol, sw1x, although the Hampton might share the very same shuttle.
All I want is a comfortable place to sleep with strong free wifi in the room, a free breakfast served at 6am and airport shuttle service for under €110/night.
If I miss that shuttle, the next one to the Hampton is at 20:20.