Congratulations on your engagement and forthcoming marriage! :-) You're doing the right thing so far -- looking at what you really want, and figuring out how to get it.
Since you're wanting a small affair and very casual, you could get married at the Courthouse with a Justice of the Peace with your close friends in attendance. Or you can see if the JP or a local minister would do the honors in another location like your home or a friend's home, or even something like a local reception hall or something. Many pastors will not marry those whom they don't know, or who are not members of their church; but some will. You may or may not find an accommodating church -- many churches will only allow their facilities to be used by their members; plus with Mar 17 being a Wednesday, many churches have youth meetings or other meetings that day, so may not have space available.
I'm leaning more towards a small home wedding with a judge officiating -- you may need to check your state laws about who is authorized to perform a wedding. In my state (Mississippi), a blood test is required to check for STDs, plus the couple must apply for the marriage license at least 3 weeks or perhaps 30 days prior to the actual wedding, so you'd want to check to make sure you get everything done right. Because my sister was too young to marry without parental consent (age 21 in MS), she and her now-ex-husband crossed the state line into TN (age 18 is the minimum there) where they went to a courthouse and got married on the courthouse steps -- there was no waiting period or anything. If you find that your state has too many restrictions, or you're having trouble lining up a minister or judge, you may be able to get married in another state.
Or perhaps you'd like a courthouse wedding with a party or reception at your home or a friend's home. Most people used to get married at their homes, surrounded by their friends and family, and that sounds like a fun idea to me.