I think of fingerstyle guitar playing as having three possibilities: no picks, thumb pick and bare fingers, thumb pick and fingerpicks. The type of music you are playing will determine which is best.
The recommendations I make come from someone who simply can't grow nails sufficiently long/strong enough to use for guitar play.
The great bare finger players we discuss all play amplified, and that makes a huge difference. They probably have fake nails, too. Unamplified, bare flesh can sound dull and quiet. Also, I've found that some guitars are more responsive than others to fingerpicking, some need amplification to sound good, and some just need picks to sing.
My suggestion is that you start with bare fingers and bare thumb.
Then, try adding a thumbpick. I like the Fred Kelly Bumble-bee:
http://fredkellypicks.com/bumble-bee.html
and the Fred Kelly Speed:
http://fredkellypicks.com/speed.html
Learn how to control the thumbpick tone with palm muting.
Next, add the Fingertone picks as Howard recommended:
http://www.guptillmusic.com/propik/fingertone.html
When you are ready for heavenly fingerpicking tone, try plastic picks, like this:
http://www.jimdunlop.com/product/cle...ic-fingerpicks
Unlike the metal picks that you bend to conform to your fingers, let the plastic tips extend past your fingers. It takes a different mind set to play this way. Think of the picks as leverage tools. Kind of like when you use a wrench to loosen a bolt, you don't need to have your fingers touching the bolt.
All that said, I find fingerpicks to be fussy and uncomfortable, so I've tried to emulate fingerstyle with a flatpick, as Davis Webb said above. But there are things I can do with fingerstyle that I haven't been able to duplicate with a flatpick, so round and round I go.