Late September / early October is a great time on the Camino, I think my favorite. How fantastic!
Of the approximately 300 albergues on the
Camino Frances, roughly half can be booked in advance (according to this site:
http://caminodesantiago.consumer.es/albergues/#camino-frances). But at that time of year, you won't need to worry about booking, at all. If you get in with a large group that is moving at the same pace as you, you may find the albergues filling up. If this happens, just stop sooner for one day, and you will find you have no problem finding a bed.
If you plan to stay at hostales (small hotels), pensions, or hotels instead of albergues, you usually will not need to book at this time of year. The only time to be concerned at non-albergue places is if there is a holiday that falls on or near a weekend. Then the hotels likely will be full and your best choice will be an albergue.
As for luggage transfer, you arrange this each day, as you go. The hospitalero or hotel reception will instruct you on how to prepare your bag and where to leave it for pick up. The catch is that you have to know where you are going that day, so the bag will be delivered to the right place. Not all albergues accept pilgrims using luggage transfer services, so be sure to ask your host. The cost is usually around 7-8 euros.