I disagree with all who said that you should fully explore the 2-finger technique before moving on. From what I've seen, it's much easier to develop a new playing technique early on.
I'm also a firm believer that 3-fingers is superior to 2-fingers in almost all fields. When it comes to 4-fingers, I'm not so sure. While your Index, Middle and Ring are fairly similar fingers in strenght and lenght, neither your pinky or thumb is anatomically similar to those three. Hence, your plucking tehcnique becomes very different, and it's harder to judge if it's "superior". I've added the thumb to my technique, but I'm often alternating between 3 and 4, depending on the line thats is played.
Anyway (enough rambling), I highly recommend getting used to three or 4 fingers early on. For three fingers, I recommend practicing all you do with the Ring-Middle-Index pattern, until it becomes more natural to you to pluck with three than with two. Practicing everything, from scales to full songs, should be done with three fingers, so it becomes more natural.
As for 4 fingers, it's similar. I recommend going Ring-Middle-Index-Thumb, or perhaps T-I-M-R. Your thumb being more precise and strong than your pinky, I don't really think training the pinky is a good idea.
Of course, you mentioned you think you may have a flexibility problem in your hand. Your Middle and Ring fingers are linked, but still, it's weird that you can't do a "gun". Perhaps consulting a professional would help. If you really have problems with your Ring Finger, then there is another way to play with three fingers: Thumb-Middle-Index.
Once again, the key word is practice. practice all your lines, warm-ups etc with your new technique, slower at first if you need, and do so until it becomes natural. Find out what areas are causing problems and practice exercices in that specific area (string crossing, keeping a constant sound, etc).
The most important thing, however, is never play if it really hurts. This potentially means that there is a physical problem lying underneath, and should be treated/identified ASAP.
I hope this helped.