I'm looking to get the train from Beijing to Ulan Bator, stay a week, then get back on the train to Irkutsk, stay a week, then get back on the train to Novosibirsk. The see what happens from there..any advice re train travel and how to go about it?
Just go! I did much the same trip as you're planning (though I ended up staying two weeks in Irkutsk /Olkhon Is.) a few years back. Depending when you travel, about the only planning necessary is to book hostels in UB and Irkutsk. Load up on train food, get off the train at the Mongolian border (where carriages are lifted off the bogies and set down on another set to suit the different rail gauge) because it's a good way to meet other people/travellers on the same trip as you.
Most of all, pack a sense of humour and enjoy yourself!
Oh, and take plenty of photos about 5 years ago