Sounds like a great trip!

I took the train St Petersburg > Moscow > Beijiing (> Shanghai) a couple of years ago. It was a fantastic experience.

We had no trouble just buying tickets as we went along. Well, thats not strictly true, we spent a good half an hour at each ticket window negotiating, but we got the tickets in the end! All part of the fun. If you teach yourself the Cyrillic alphabet and spend a few minutes studying the timetable (online or in the station hall) you'll be pretty well armed. Getting the train number and departure time is key, then you can write this on a piece of paper to show at the window if necessary.

We also found that things got easier and people got more interesting (and interested) as we went southeast. (Things also got warmer, which was nice, since it was December.)

I believe that the 'real' Trans Siberian can get pretty busy in summer. But if you're stopping off on the way, you may find that you're travelling on other trains, which are less busy.

Echo the recommendation for Seat 61. Have fun!