My first punt I was shitting myself on the walk-up, a real case of rubber legs! I think this is quite a normal feeling if you've not done this before.
I did a load of research before my first FS. Settled on a very well reviewed SP who appealed to me; check the Puntingwiki links in your area (links above reviews) as they tend to have a "league table" of reviewed SPs. This'll increase the chances that your first punt will be a good one.
Just keep the booking simple with regards to services, this will reduce the pressure you'll place on yourself. Don't worry about her satisfaction, just concentrate on you. As mentioned above, an hour would be a good length as well.
I did mention in my booking that it was my first time seeing an escort - as she was an experienced (ex-parlour) SP, she was able to guide me through it all, taking the pressure off me. This might be something worth considering as well.
If you've not, have good read through the puntingwiki for more "new punter" guidance.
Perhaps to help distract your mind, make the punt part of a series of events. Research a cafe to visit before the punt, grabbing a drink and use the toilet there. Also sort somewhere to eat after the punt. This might help take your mind off things.