Best way to go in Koh Samui from Bangkok

There are several ways you can do the trip. Bus/ferry, train/bus/ferry or fly.
Here is a complete breakdown of timetables and costs using various means of travel.
Enjoy your trip.

Thanks mate, I really appreciate. Have a good day

hello,

I also recommend the Lomprayah ferries to visit Koh Samui or the other islands (Koh Tao, Koh Phangan) from there.
lomprayah.com

As you have only a few days in Bangkok I would look at flying down to either Surat Thani with Thai Lion Air and getting the ferry over to Samui for about 2,700 THB return or if you aren't worried about the cost you can fly direct with Bangkok Air to Samui for about 13,000 THB return.

Good luck with your travels.

Air Asia will fly to Surat Thani with bus/boat connection and Nok Air will fly to both Surat Thani and Nakhon Si Thammarat with a bus/boat connection to Samui