Different types of picks produce different sounds, and pick choice might depend upon whether the autoharp is played lap style or Appalachian style (held upright). Generally a felt pick is just elementary strumming. It's nice but not seriously playing the autoharp. To get any melody from the autoharp one has to be able to accent specific strings, so finger picks or reinforced fingernails are usually in order.
Among the finger picks, there are two principal kinds, each with its own effect. I suggest a plastic thumb pick with broad, long blade in any case, but the fingers can use plastic or metal picks. The plastic picks are generally more pleasant in sound. The metal picks allow more precise picking and getting maximum volume from the instrument. So one can decide to be a finesse player or a slugger or switch back and forth.
The number of finger picks to wear is a good question. I think it will be found essential to use the index and middle finger. The ring finger and sometimes the pinky are used by some players but usually at more advanced levels of playing. Start with the two primary fingers and then find your own personal needs from there.
The thumb pick is for playing rhythm in the bass strings. It is meant for playing in only one direction, low to high, but will be the opposite direction of the finger picks. The finger picks are designed to cover the finger tips, not to be finger nail substitutes. This is mentioned because one unfamiliar with finger picks will often try to put them on backward when first handling them with curiosity. They are not quills so much as finger guards. It is the metal picks that really have a blade to them.
There aren't many choices among plastic finger picks, but among the metal picks the ones I recommend as the most comfortable are ProPik "split wraps". The choice of brass over nickel will sound a bit less metallic. ProPiks are heavy weight material, their .025 thickness being equivalent to Dunlop's heaviest grade pick. For a bit better feel of the strings I prefer the Dunlop brass picks in .018 or .020, the heavier one holding the fit adjustment better and lasting longer.
Metal finger picks require that one keep a small file to dress the edges. As the picks wear against the strings, the edges take on a knife blade and then roll into a coarse burr on the finger side. Eventually a pick will become too short and will need to be replaced.