Customer care services give you much more than answering services can.
Sell your products
Resolve technical and general queries
Provide analysis and reports
And much more
Using a CC service can give your new business a competitive edge as this is usually provided 24 hour per day via telephone or internet.
The advantages of a customer solutions Vs answering service are endless.
Good quality service can be found and various payment options are available, per call, hourly, weekly, monthly etc...
There are customer care solutions out there that give you great value for money
I say, try to automate it as much as possible. Have a form on your site that customers can fill out and have a way where you can get the messages directly to your phone so you can respond quickly.
If you have to get a phone number, try gotvmail.com it is a great service where you can have the calls forwarded to your phone or even have a voice mail talk for you like you are a big organization. It is dirt cheap and should do the job.