Can you suggest a company to use for a private company from SIN to the city

Sorry meant private TRANSFER

Just follow the signs and take a taxi. The airport is very close to the city and the taxis are clean and the lines efficient.

Do they take credit cards, or need I get local currency?

The taxi drivers were in a dispute with Visa/MC last I heard, so they would't take those cards, but they would take AmEx. But you can get Singapore dollars from an ATM in the airport... You'll need some eventually.

Agree with Kathie, taxis lines are very efficient, ( although can be long at peak times) there are plenty of ATMs at the airport it will cost about S$20/25 dependant on where in the city

I'd definitely take a taxi. I've never used a private service to go into the city in Singapore. it's not necessary even if such exists. Or if you're staying at a hotel and one that's on the MRT line, then the MRT works out really well. I've also taken it from and to the airport when staying at The Fairmont Hotel for example.

Happy Travels!

Absolutely take a taxi. After midnight the fare is double, but still very reasonable.