I did it last August. We got the ferry from Japan to Vladivostok. Bought the tickets at the station for the next night (on both occasions), did it in two sections. Vladivostok - Irkutsk and Irkutsk - Moscow. Tickets were cheap for 4 berth. about 300 dollars. We had the berth to ourselves for first section, shared with russians on the second. The train journey times were 71 hours for the first section, 84 for the second. We didnt get the quickest trains though or the touristy ones (train no's 1/2 or 7/8- those with a single digit), but we didnt care.
Its probably the most relaxing thing I have ever done in my life. Bring lots of books, scrabble, backgammon etc. The train stops pretty much every 2 hours or so for 10 mins and can stop for upto 45 mins at big stations. You can print off timetables in English from a website.
The lonely planet forum is excellent for all info on the trans siberian.
http://thorntree.lonelyplanet.com/categories.cfm?catid=19
Also we had bryn thomas's guide for the trans siberian which was excellent http://www.amazon.com/gp/product/1873756704/ref=pd_bxgy_img_b/104-6305180-9030367?%5Fencoding=UTF8
Food wise, we found the food off the train excellent. Great thing was if you were looking for food in the morning, there seemed to be bread, salami etc. In the evening the people selling food would have prepared meals (meat, veg, spuds) for like 2 dollars or something. We brought loads of salami, olives and general nice deli bits. you can buy all the staples at the stations when it stops.
As for dodginess, moscow is a bit sketchy but like anyplace when you travel, keep your eyes open. irkutsk was fine, a small city. Vladivostok was also fine.
I would have reservations bringing kids. There were lots of russian kids on the trains and they whiled their time away running up and down and getting off at the stations, but it does involve alot of time looking out the windows/reflecting, which kids aren't particularly good at.
We continued the train ride Tto germany which is only two extra nights stoping of in st>petersburg and riga which is well worth it> then get your ryanair flight from wherever!