Here is the English translation of the interlinear version of 1 Peter 3:3-4 in the New American Standard:
Whose let it be not the external of braiding of hair and putting around of gold or putting on of garments adorning1
But the hidden of the heart man in the imperishable [beauty] of the gentle and quiet spirit which is before God of great worth
By taking the verse apart in the following way, I think we can better appreciate how Peter in thinking in this verse:
The adornment of what is external: NOT SIGNIFICANT
- braided hair
- gold (jewelry)
- (fine) clothes
The adornment of what is internal: VERY SIGNIFICANT
- imperishable quality
- tranquil and gentle spirit
- precious to God
There is clearly a contrast here between the two types of adornment: one is purely physical and outward, while the other is spiritual and inward.
Frankly, the word fine is not needed to make sense of the contrast Peter is painting with his words. The contrast comprises, on the one hand, adornment which is external and expensive, yet ultimately perishable. On the other hand,
there is adornment which is costly (but costly to women only in terms of the discipline required for holy living), internal, and imperishable, as is all our treasure in heaven (see Matthew 6:20).
The perishable includes elaborate hairstyles, gold (i.e., gold jewelry, another word which is inserted in English versions, and even though it is not in the Greek text, the word peritheseos is, meaning "putting around," which suggests necklaces, bracelets, and the like), and clothing. This last item, as has been pointed out by @JonathanChell, above, makes sense only as fine clothes. In fact, the thematic element in Peter's contrast is adornment, which in our English language means "that which lends beauty to or enhances aesthetically." Implied, then, is finery, not rags!
In conclusion, Peter is obviously talking about two types of adornment: One is outward and attractive; that is, carefully coiffed, ostentatious, and perhaps even garish; while the other is inward and precious; that is, hidden, spiritual, and precious in God's sight. This last characteristic takes us all the way back to God's instructions to the prophet Samuel concerning his selection of David as King Saul's successor:
"'Do not look at his [i.e., Saul's] appearance or at the height of his stature, because I have rejected him; for God sees not as man sees, for man looks at the outward appearance, but the LORD looks at the heart'" (1 Samuel 16:7 NASB Updated).
As Jesus said of the Pharisees and their insistence on outward and noticeable acts of piety and the external aspects of religion:
"They have their reward in full [here on earth]" (Matthew 6:2, 5, and 16).
Likewise, the women in a local assembly of Christians can dress to the nines and have their public reward in full, or they can dress modestly in public but reap a reward both here and now by nurturing their inner character so as to please the Lord.
1"adorning" = Gk. kosmos; compare 1 Timothy 2:9, where "to adorn" = Gk. kosmein