Osaka-Kyoto area travel passes?

Hello everyone,

We are traveling to Japan soon for the first time, and (like many folks) are finding the transportation a little hard to understand.

We are flying in to Osaka, staying in Osaka for 4 days, and then finishing our trip in Tokyo and flying out from there. Since we are only going one-way on the high speed rail, it seems like it is not worth it to buy the JR Pass. How far in advance do we need to buy our train tickets? We will be going between Osaka and Tokyo on a Tuesday (hopefully afternoon or evening).

I have also found a few options for discount travel/tourism passes in and around Osaka. They are not JR passes, but I was hoping someone here might have some advice for us about which, if any, of these to buy. The links are as follows:

Osaka Visitor's Ticket (we live in Taiwan so we can buy this before we reach Japan)
http://www.kotsu.city.osaka.lg.jp/foreign/english/ticket/visitors.html

Osaka Unlimited Pass
http://www.osaka-info.jp/osp/en/

Kansai Thru Pass
http://www.surutto.com/tickets/kansai_thru_english.html

For this leg of the trip, Osaka is our home base, and we are planning on going to the aquarium in Osaka as well as the Osaka Castle, and then day trips to Nara and Kyoto.

Thanks for reading and for any advice you can give us!

-Sarah