Hello and thank you!
The Tempozan Metro station is actually not far away from the pier. Maybe five minutes on foot. The trains, incl. Shinkansen, are fairly inexpensive. Japan is the land of trains. The total time to Kyoto is probably around an hour. The Shinkansen part is only 15 minutes or so.
However, I would strongly recommend hiring a guide. Since this is your first visit to Japan and Kyoto, you would spend too much time trying to figure out how to get from A to B. Kyoto has so much to offer. We have now been there three times and we still haven’t seen it all. The individual sites are not very close to each other, so it’s really the best to hire a guide, arrange a tour with him and just follow his lead instead of wasting time on figuring out which train to take and were to go. I am no fan of Celebrity tours at all so I can only recommend taking a private guide. I can highly recommend Koichi, with whom we booked our tours over the last cruises. I can give you his contact information.
Since this report a few others followed my recommendation and toured with Kochi. All came back very happy.
Osaka on the other hand is very easy to do on your own. Walk to the train station take the train to the castle, walk around, visit the castle and then take a train to the Dotonbori area to enjoy the weird and entertaining buzz. Koichi also offers tours in Osaka, but contrary to Kyoto, I‘d say you can easily do it on your own.
The best way to find the right train connection is Google Maps or Apple Maps. The pricing is not really a problem because the Metro rides are only between 1 and 4 USD. I used an Airalo eSim so we always had internet to look at maps and connections etc.
Oliver