You have not said where else you will be, but in any event, stay an extra day and do Cano Negro for the wildlife.
You do not have to book ahead unless you are there during Semana Santa or Christmas which you are not or possibly if arriving late on the first day and want to do a tour the next day. Usually your hotel can book for you and if, for some reason, they do not you can call yourself. However, given that you are only in La Fortuna effectively one day, you may want to have everything arranged in advance.
Any tour will almost always pick you up although they will likely charge you extra for pickups in El Castillo. However, I seem to recall that one of the zipline, hanging bridges companies is quite close to El Castillo.
Again, in El Castillo, you will not be flagging down taxis: El Castillo is a small village at the end of a long teeth chateringly rough road. There is a great butterfly and reptile exhibit.
As for booking a tour on the day you arrive, you might choose to risk it, but you will not get out of SJO likely before 1330 assuming your flight arrives on time); it is about 3 hours to La Fortuna and another approximately 1/2 hour to El Castillo. Assuming that after flying from somewhere and getting to your hotel, you still want to go on a tour, be sure that pickup is 1800 or later, not that the tour starts at 1800. Consider that if you are being picked up in El Castillo, pickups will generally be earlier. Consider finally that it will be dark at 1800 so I am curious what tours you will take, other than to see the volcano which you may see from your hotel in any event.