There is a popular sentiment circulating throughout high schools and colleges that the original colonists were only secular, irreligious, rapacious.  However,  their own testimonials, from two primary sources, show that they were not.  True, they made mistakes, and some were greedy, but they repented of their flaws after twelve years of hardships.

First, they tried early on to build a church of brick but settled for one made of wood: "true it is that there was a Brick Church intended to be built, but not so much as the foundation thereof ever finished, but we contenting ourselves with a church of wood[.]"

Next, they thanked God for the help of the natives: 

[S]o that had not God, by his great providence, moved the Indians, then our utter enemies, to bring us relief, we had all utterly by famine perished. How unable so small a Company of people, so poorly sent over, were to make way for such as should follow, may easily be judged.

Unfortunately, in 1622, the natives attacked the colonists and wiped out one quarter of them because the natives saw that the new arrivals were taking their land.  That's simply what happens in all migrations to the New World and even around the globe – even the Puritans and pilgrims fought with the natives over land disputes.  But by and large, the leaders in the Virginia colony tried to get along with the natives at first and whenever possible.  

For example, Capt. John Martin took some possessions from the Indians, and the Assembly, America's first true democratically elected institution because its members were voted for out of various districts and plantations, rebuked Martin:

It was also ordered by the Assembly the same day that in case Captain Martin and the gang of his shallop could not thoroughly answer an accusation of an outrage committed ... he should from henceforth take leave of the Governor [Sir George Yardley] as other men and should put in security that his people shall commit no such outrage anymore [against the Natives]. (Source)

In other words, Capt. Martin could not become a "lone ranger" and trade with Indians without permission, since the English-native relations were precarious and especially since he committed an "outrage" against them, which the governor, his council, and the Assembly corrected.

And finally, in this passage, the Virginia colonists acknowledge their greed as a sin:

But amidst this happiness was the hand of God set against us, in great part, no doubt, for the punishment of our ingratitude in not being thankful but forgetful that by his mercy we were delivered from such bondage and calamity as before time we had suffered [from the first governor,John Smyth]. Justly likewise were we punished for our greedy desires of present [immediate] gain and profit, wherein many showed themselves insatiable and covetous[.] (Source)

Their theology was simple, perhaps simplistic: the hand of God turned against them because they were not thankful, but covetous.  Regardless, their hearts turned back toward God.

No, the original colonists did not achieve moral perfection, but who ever does?  Not even the natives could achieve it.  But the colonists set themselves on the right path during extremely difficult times and hardships.

James Arlandson's website is Live as Free People, where he has posted original sources on Jamestowne.