We arrived at T1 on a United flight that landed around 8:30am. We had plenty of time to get through customs and take the airport shuttle to T4. We just walked out to the kiosk and bought tickets on the 10:45 bus. If I recall correctly, the kiosk required cash (in Euros), so if you don't bring some Euros with you from home, stop at any ATM in the terminal and exchange there -- you'll need them from then on anyway. We did not make advance reservations for the bus, but that would be an option if you're confident that your arrival time will not be delayed and cause you to miss the bus. I would advise taking a snack and a bottle of water onto the bus with you, because as I recall the stop in Soria was very brief and there wasn't time to get anything for lunch during the transfer. Other than that, I agree with Mark that the bus was an inexpensive and comfortable way to get to Pamplona.
You can also buy tickets at the Pamplona bus station for the bus to SJPP, but it may not be possible to make a same-day connection. Check the schedule on that. But the worst thing that could happen is that you'd spend the night in Pamplona and catch up on jet lag before heading up to SJPP the next day. We actually pre-planned a night in Pamplona for this reason.
Buen Camino!
Jim