Well, before you taking a Trans-Siberian I would recommend you to spend some time in the European part of Russia: Moscow, Golden Ring, Yasnaya Polyana... Then you can take a Trans-Siberian train and head to the East. Definitely go to lake Baikal, I would go there at least for 3-4 days... Spend more time there if you have a chance, it is a such a unique place.
It would be kind of complicated to visit all the places that you mentioned, like if you'll go to Kamchatka and Tuva after Baikal and Irkutsk and then to the South (Black sea coast).. Hmmm... It will cost you so much money. I mean it is up to you but I would skip skip Kamchatka and Tuva and would just fly from Irkutsk to Sochi and there you can spend like a week. If you like skiing you can check Rosa Khutor ski resort near Sochi (resort was built for the Olympic Games). It's really nice there, but pretty expensive.
And from Sochi/Krasnodar area you can go to St. Petersburg. Spend there as much time as you can - it is my favorite city in Russia and it's so much to do and see there. From St. Pete take a Sapsan train to Moscow and then fly back home :)
It would be my itinerary, something like that :). If you want I can help you to plan your trip with more details, you can contact me through the message and I'll be happy to help.