I'm aware there isn't that much information available on here about arriving at Ancona then getting to the central train station in Ancona, so thought I'd add my experience as best I can remember it:
We arrived in Ancona after around 2ish hours delay (Ryan Air from Stanstead). By then it was lunchtime and obviously very hot. We went next door to the departures building (which seemed to take forever with our cases because it was so hot, but in reality it didn't take that long - we were just tired, hot, hungry). I'd read on here to go to departures to buy tickets for the bus, which according to my internet research was the no. 38 bus that went to Ancona Centrale stazione. However, the place to buy the tickert was closed (for lunch) and two ladies in a shop told me it was not possible to purchase any bus tickets until after lunch (I imagine that means a miniumum of 16:00 hrs). They also told me that there was no bus number 38, just a bus to the station (so don't bother asking for numbers, just ask for location). However I was then told there was no bus for many hours as it was lunchtime. So the only other option (apart from very infrequent trains from tiny station opposite) was to get a taxi to Ancona Central station. I can't remember how much he charged me but I do remember being shocked at the amount - and then I realised - I was a captive to the cost because I had no other choice. I think I paid around Euro 25.00-35.00 ish amount. The taxi driver then told me on our journey that our plane was late and now it was taking off late. They must rub their hands with glee when a plane is delayed. However, they've got to make a living and in many people's eyes the amount we were charged isn't a lot of money, but to others (i.e. myself on a budget) it was quite a lot just to travel to the main train station. Now I've typed that it doesn't seem a lot of money at all - at the time I guess I was expecting to just pay a small amount for a bus.
Clearance through the airport to collect bags/go through passport control took about 40 minutes. But we were delayed and may have landed at similar time to another flight.
So I hope this information helps others, in the future.Edited: 19 August 2014, 14:46