A couple friends and I are planning a trip to Mongolia for the October holiday. The information I can find on getting to Ulaanbaatar direct by train seems to say there are trains on Tuesdays and Wednesdays but I can't figure out a price. Has anyone done this trip recently and can offer advice? There also seems to be a route where you fly to the border, walk across, and take a train to Ulaanbaatar from there. Has anyone done this method and is there anything to see between the border crossing and Ulaanbaatar? Any advice would be appreciated. Also, any good Mongolia tips in general would help as well. Thanks!

Matt