Seriously, if neither of you are affiliated with a church, just go with a JP or an ordained minister. I had a friend who got married and the Minister was also the DJ at the reception. The entire thing took place at a fire hall and it was really nice.
If you get married at the courthouse in Leonardtown you can get married under the tree out front. I know a couple that had a very pretty ceremony with the fancy white wedding dress and a whole procession of bridesmaids and groomsmen.
United Methodist Church of La Plata I believe is open to everyone. Church is a little big to me, but if you want to be in a church it is the way to go. Catholic will not do unless you are Catholic and then they don't always allow unless you belong to that church.
Be open be honest and you will find the correct people to perform your ceremony.