Wanting to do this journey in November and looking for any tips that can help from people who have done it. I am not in a rush. Also can the Mongolian and China visa be got on the train at the border? Some say yes some say no.
Seat61 is the best site concerning train travel in Europe. It also has a section about a train travel from London to Peking.
There are a lot of practical tips, hints and suggestions. A very detailed section also covers the Visa details of all countries you travel trough.
Since you're looking to do it "on the cheap", here are some money-saving tips:
The best tip I know of is to use the cheaper local trains only (ones that don't cross international borders) to get right up to the border, then cross the border on land, and continue by train on the other side. (Wikitravel has plenty of info on both Russia/Mongolia and Mongolia/China land crossings, I've done China into Mongolia at Erlian myself and it was easy). This also allows you to use the cheaper "platzkart" (open compartment) trains instead of "kupe" (closed compartment) ones, which are a must if you want to truly experience Russian train travel. There's some talk in Russia of phasing out "platzkart" trains, so it's all the more reason to try them out before they're gone - it's the way most Russians travel (and used to travel in Soviet times) - it's kind of the equivalent of economy-class flights in the US, the "standard mode of long-distance transportation".
Another money-saving tip: There are very active CouchSurfing communities in most Russian cities along the Trans-Siberian (I have not checked this in China and Mongolia, but there it's generally not a problem to find cheap accommodations anyway).