eloping questions

Hi, so my fiancé are thinking about doing a courthouse wedding then getting a dress off of Amazon, renting a tux & getting professional pictures done. We don't want a big wedding & we're on a budget. I live in NE Ohio & originally wanted fall photos but now I want snow photos. (plus we have a lot of fall/December birthdays). I was thinking sometime in February. When would I have to apply for the marriage license & is there a time limit? Also, if we get married in February how would that affect taxes? Would we still claim single?