There are at least two schools of thought, or should I say technique, when it comes to hand positions. Unlike your choice to use a thumbpick or not, this decision can effect your advancement down the road. The two positions in question here can be summed up simply with the words: To plant or not to plant.
In the beginning it feels natural to plant your ring and pinky fingers (or even the base of your hand) on the guitar for two reasons: stability and to guide your fingers over the appropriate strings. This will expedite the learning process but it’s a hard habit to break once you’ve started and I recommend taking the extra time to learn not to plant, it will pay off in the long run. One of the major cons of this method is that you are essentially cutting off some of your fingers. This is not to say you can’t play like this, Merle Travis and Reverend Gary Davis both played with only their thumb and index fingers so it’s not improbable that you will get to where you want to be, but you are not them, you are you, so try to think about what could be using all four fingers.
Not planting, commonly known as the standard classical technique, is the preferred route for many reasons. You can choose to play with one or two fingers this way as well, but you now have the option to go where it takes you without this self-imposed boundary. There are many resources to be found which deal the subject of position and posture in great detail so for the purpose of getting started properly this will be a quick overview.
The goal is to sit ergonomically correct, this will facilitate long sessions with no unnecessary fatigue on your back, shoulders or wrist. Sit up straight in an armless chair; hold the guitar in your lap so it sits on your right leg and the top of the back is against your body. I prefer to have the guitar tilted back slightly. Raise the neck a little so your left elbow isn’t resting on your leg. Rest your right forearm across the top of the guitar so that your hand is over bottom of the sound hole or if your guitar has F Holes above the bridge a few inches. The thumb remains straight while the fingers should be slightly bent. The key is comfort, use this as a guide to start with and find your position.
A quick note about the fingers
A good place to begin is to hold your thumb over the 6th string (the low E) and hold your index finger over the G, middle over the B, and ring over the high E. This isn’t to say those strings are attached to those fingers, its just a comfortable place to begin getting your hand in tune. The standard classical fingering is a little different, with the index assigned to the D string and the other fingers all move up a string, ending with the pinky assigned to the high E. If that feels more comfortable for you use it instead. The fingers should curve in slightly and never bend backwards when you pick the strings.
A few more words on playing guitar in general, not restricted to fingerstyle
The left hand: Try not to make a habit of anchoring your thumb on the back of the neck. It’s good for guiding the hand, but you will need to wrap your thumb around the neck to finger some notes on the Low E string soon. Also, try and hold down strings using the very tip of your finger, there will be much better control of your tone and it will be less likely to interfere with the ringing of the adjacent strings.
Avoid using excess force when hitting the strings unless you’re going for a unique effect. Try this little experiment: Hold down a chord using as little pressure as you can, barely pressing the strings, and strum gently. Most likely you’ll hear some muted notes. Increase the pressure slightly, applying a tiny bit more pressure until every note of the chord rings out. Now you’ll begin to realize how little pressure you need to use. Listen carefully to this chord. Now hold it down as hard as you can and strum again, do you hear any difference? Don’t waste your energy.