What type of train ticket should i buy?

Hi! My family and i will be travelling on a 6 day trip to Japan, Osaka. During our trip, we plan go to places in Osaka such as cup noodle museum(Osaka), Osaka castle, Rinku premium outlet, Universal Studios Japan.

In Kyoto, we plan to spent a whole day there so places that we would want to visit is Kiyomizu-dera, Fushimi Inari-taisha and Arashiyama

In Nara, we plan to visit the Nara Deer Park and might spend half a day and go back to Osaka for other activities.

I am still quite clueless on what type of pass to buy because i am confuse about the train system in Osaka. I will be staying at the area in Nagahoribashi and is a subway station, but other places that i am visiting needs either a JR pass, or a private railway, etc

Any suggestion or advice on which pass i should get and which is place to visit first better to save the cost?
Is there any route that i am visiting allows us to take the bullet train? I would like to take a ride on the bullet train maybe to Kyoto from Osaka and how is the price range as compared to normal train passes?

I would also like to get your advice if the places that i go and the pass that need to buy to be able to access the places will be cheap and fast way to get there.

Itinerary:

Day 1: Touch down on 1235, visit Rinku premium outlet and back to apartment at Nagahoribashi
Day 2: Universal Studio Japan
Day 3: Osaka castle, cup noodle museum
Day 4: Kyoto
Day 5: Nara Park
Day 6: Morning flight at 1000

Till now, this are places that i roughly plan to go but i think there are some days that i can add other activities in.

Thank you in advance :)