dakota,
Congratulations on your engagement!
If she marries in the States while she is here on a non-immigrant visa, she has two choices. She can stay here and apply for adjustment of status or she can return home and wait while you petition her for a spousal visa (CR-1/K-3).
Like William mentioned above, if she leaves the country after marrying, then it is fairly likely that she will not be permitted to re-enter on her current non-immigrant visas. After she is married to you, she becomes an intending immigrant and her student/journalist visas are not going to guarantee her entry.
Before you do anything, I would invest in a consultation with an experienced immigration attorney to explore your options further. You may want to consider skipping the Stateside civil wedding and just having the church wedding down there.
On your question about which documents she will need to marry here, you should check with the local county office that issues marriage licenses for the jurisdiction where the wedding will take place. I think a certified copy of her birth certificate along with her passport or other photo ID should be plenty of documentation in most places.
Ray
