If I were you, I’d buy the 7 day Japan Rail pass and activate it on the 11th. It will definitely save you money on a Tokyo-Kyoto-Osaka-Tokyo route.
As for how to travel around inside Tokyo, I assume you are asking about buying tickets. It’s pretty simple to just buy a Suica or a Pasmo card and load it with several thousand yen. You just pass the card over sensor on the gate, and the fare is automatically deducted.
Keep in mind that there are discount tickets you can buy if you plan, for example, to use one train line for the entire day. For example, if your sightseeing route takes you all over Tokyo just using JR trains, you can buy a one-day JR ticket for 750 yen.
You can use the Hyperida route planner to check both the route and the price, and it will help you determine if the one-day ticket would save you money. www.hyperdia.com
One final thing - if you have children under 11 in your group, they get discounted tickets; and children under 6 are free. Be sure to buy a child’s pass for them.