We did the same thing in April: our family of 6 (11 year old daughter, 16 and 18 year old sons, Mrs. Beeks and I, and her mom) walked from SJPdP to Pamplona, then took the train to Sarria and finished the walk. It was our first time.
Great experience for everyone! St.Jean start, Pyrenees beauty and challenge, and we found the section from St. Jean to Pamplona very different from the final section.
We flew into Madrid in the late afternoon and spent the night. We took the train to Pamplona, then a taxi to St Jean. Went to the Pilgrim's office, then found a place to stay.
We had reserved our Madrid hotel, bought our train tickets to Pamplona, and had reserved our taxi before we left home. Also, we were going to arrive in Sarria after 9pm, so we did reserve our alburgue there. We had 4 different train segments on our trip, and we had purchased tickets for all segments before we left home. Our trip had so many moving parts (such as a post-Camino overnight in Ponferrada before heading back to Madrid) we didn't want to take any chances.
We also had reservations at Orisson but the route was closed. Bummer. We had made reservations at the municipal alburgue in Valcarlos, just in case, and we ended up there.
Orisson reservations take patience. I emailed them super early, and a few days later they replied, said to email them after November 15 for our April stay. I emailed them at the appointed time and waited for a reply. Didn't hear from them. Super anxious and wondering if I got the email address wrong, I emailed them again 5 days later. They did reply back...17 days later.
Renfe let's you purchase train tickets, but something like 62 days in advance. We attempted to purchase our tickets about a month in advance, but it was very frustrating. We would get a good price, input all the information, then find out that all those tickets at that price were sold out. Back to square one, with a higher price. Same routine... input starting point, destination, number of people, names, passport numbers, ages, etc... to be told again that all tickets at that price were sold out and start over. Prices were increasing so much it was like watching the prices at a Southern California gas pump!
We ended up at a third party website, where we found good prices and an easy purchase system with a very minimal fee. Sure, we could have waited and bought tickets at the train station the day before? We limped into Pamplona, due to a slow walker in our group, after 7pm. Plus, there was only 1 train to Sarria. Was very glad we had tickets in hand.
Plan, but don't over do it. Research, but don't overthink it. You're just walking... right?
Buen Camino!