Why would you hire a driver when it is such an easy train trip? One train change at Kufstein of 11 minutes. Very comfortable. It will take about 5 minutes, and you will be standing on the platform waiting for your Railjet train to arrive and whisk you directly to St Anton.
Edit - If you are intimidated by an 11 minute connection, you can always take the Meridian train one hour earlier and twiddle your thumbs at Kufstein station. There is the Inner Bar by the station. Open 7 am to 3 pm and 5 pm to 1:30 am. Serves lunch noon to 2 pm, and dinner 6 pm to 9 pm. Closed Sunday & Monday.
http://inner.at/
The Skiing Buddha is a Thai restaurant next to the St Anton train station. Very good. There is also an indoor tennis court, rock climbing wall, and bowling alley in the building.
http://www.skiingbuddha.at/en/
PS - There is a connection of 30 minutes at Innsbruck if you take the EC train at 1:34 pm.