A taxi from BKK to Hua Hin should not cost more than 2000THB. If people are paying 3000thb they are being ripped off. PM me and I can give U the email and tel # of an excellent driver.
If U are on a budget, a much less expensive option is to take the Airport Express bus to Victory Monument (100THB) and then a mini van to HH (180THB). Both the Express bus and the mini vans run about every 20 minutes. The mini van service starts around 6AM and runs until 8PM and takes between 21/2 to 3hrs depending on traffic.
Unless you are planning to stay for a few days in Phuket, I would recommend returning to Bangkok for a flight to Singapore.
If you have time (3days or more) you could also take the train to Singapore from HH. Overnight train to Butterworth (Penang), another overnight train Butterworth to Kuala Lumpur and on to Singapore. The connections are not great but the experience is priceless and the cost very reasonable.
Enjoy your trip.