I hate to be the bearer of bad news, but…
Can we have our wedding someplace other than a church building?
In most cases, Catholics are required to be married in a Catholic church building (see Canon 1118). There are some exceptions. When a Catholic marries someone who is not Catholic, the Catholic party may request permission from the local bishop to celebrate the wedding at the other person’s place of worship. Because Church law states that a wedding may be held in “some other suitable place” besides a Catholic church, it is technically possible that the local bishop might allow outdoor weddings, but few do.
Re: one of you being divorced:
Can we get married in the Catholic Church if one of us is divorced?
No, unless the previous marriage is found to be not valid or the former spouse has died (Canon 1085).
The marriage covenant is sealed by God, and the Church does not have the authority to dissolve it (see Catechism #1639-1640); the Church bases this on the teaching of Jesus (see Mark 10:6-12).
A new marriage is permitted, however, if the proper Church authorities determine that the previous marriage was invalid from the beginning. A declaration that the previous marriage was invalid is called a declaration of nullity, or more commonly, an annulment. An annulment is not a type of divorce, because it does not dissolve the marriage bond; it merely confirms that the marriage bond was never properly contracted in the first place.
Re: already being married in a civil ceremony:
Can we get married by a justice of the peace in a civil ceremony and then have a Catholic wedding?
The Church does not recognize a civil wedding ceremony as valid when one or both people are Catholic. If a couple are married in a civil ceremony, the Catholic person(s) are asked to refrain from receiving the Eucharist until the marriage is recognized as valid by the Church. The reason for this, in a nutshell, is that the Church recognizes marriage as a spiritual reality, not just a piece of paper or a legal formality.
If you’ve already been married in a civil ceremony, how can you have your marriage recognized as valid by the Church? Talk to your pastor, who will probably recommend a process called convalidation; it usually involves an expedited marriage preparation process (to determine that there is no impediment to the marriage) and a simple celebration of the sacrament of marriage so that the consent of the couple to be married can be witnessed by the Church. Another process, called radical sanation, may sometimes be used to recognize a marriage as valid without a formal exchange of consent (vows).
While you may be (understandably) eager to be married as soon as possible, giving your whole selves to one another for the rest of your lives is a huge commitment—and a much greater challenge than waiting to be married. Taking the time to prepare for that lifelong giving through the sacrament of marriage will ultimately make your marriage stronger and richer.
Your best bet, I think, would be to speak with your priest and let him know the situation and your intentions. They can guide you towards the best option for you.