From Kumamoto to Nagasaki via shimabara?

I'm travelling to Japan in September. I would like to take the ferry at Kumamoto port to shimabara Nagasaki,obviously it's the shortest and cheapest way.
I would like to know how far is the harbour from kumamoto to city?
When i arrive at Shimabara port how will i get to Nagasaki? how long it takes and how much it costs?
Is the harbour far from Nagasaki railway station?
Thank you in advance for your help.

obviously it's the shortest and cheapest way.

Really? I suspect that the direct highway bus is fasteer and cheaper.

I would like to know how far is the harbour from kumamoto to city?

20-25 minutes by bus.

When i arrive at Shimabara port how will i get to Nagasaki?

By train via Isahaya (from Shimabara-Gaiko Station near the ferry terminal to Nagasaki Station). You can look up train fares and timetables here:
http://www.jorudan.co.jp/english/norikae/

Is the harbour far from Nagasaki railway station?

Shimabara Port is almost a two hour train ride from Nagasaki Station.

Faced with the same situation recently, we decided on the bus - it was fine. Shimabara is said to be nice, but there's a bit of shuffling the ferry, busses etc. and a bit of extra time involved.