What kind of ticket should I get?

Hello,
I will be traveling to Japan in late September for 13 days. I plan to stay in Tokyo for 10 of those and in Osaka for 2, taking the Shinkansen to get there. I know I will need access to the Toei Subway, since it's the closest to the hostel I will be staying in. However, due to my travel plans, I believe I would greatly benefit from being able to use the Tokyo Subway as well. Given that I will use transportation at least twice a day for the duration of my stay, I was wondering what would be the best pass for me to purchase.
Being able to use it in Osaka as well would be ideal, but not mandatory. I realize that the pasmo pass would probably work there too, but I'm not sure if they will charge me fully for all the trips, and that, if so, it wouldn't be more beneficiary to get the 3 day pass.

I will greatly appreciate any help, thank you very much.

With just two rides per day, a Pasmo or Suica card is likely to be cheapest. And it is generally the most convenient. It can also be used in Osaka.