I rarely travel by bus (except where there is no other means like to the Cambodia boarder) and mini buses are usually just too packed so will not comment on those. Both the train and a car/taxi/limo are the best way to get to Hua Hin in my opinion. The early morning 2nd class a/c coach (diesel rail car) leaves just after 8 and get into HH 3 hrs later. Cost around 382 baht.
The most comfortable way is by car which should take 21/2-3 hrs. Cost can vary but will be between 2400-3000 baht range. A good company is Oriental Escape - ::: HUA HIN TRANSFER & TRANSPORTATION SERVICE ::: Private Car & Van Pick-up from Bangkok Suvarnabhumi Airport - Cha-am, Hua Hin, Pranburi which charges 2600 for car and 3200 for van.