Should I save or pay off debt?

Me and my husband just got married and I had to use my credit card a little towards the end of the wedding planning. Now that the wedding is over, I'm trying to decide whether I should save or pay off debt. I have a little credit card debt and my husband is in his last semester of school. So our plan is to spend the rest of the year paying off the credit card debt and paying off his last semester of school. The only debt we'll have come January is our student loan debt. But our student loan debt isn't even that much. I owe 10,200 and my fiance only owe $3000. However, we do not have a savings at all. I wanted to build an emergency savings, a savings for a down payment on a home and then our separate savings. Our emergency savings and savings for a down payment on a home will be our joint savings and then we'll have our own separate savings. Is it a good idea to just pay a little more than the minimum on our student loans and put the bulk of our money into savings. I feel so stupid that I didn't work on this earlier. I'm 25 and he's 27 and we weren't saving because we were traveling a lot, we moved twice, and we had a wedding. Now that that's done, I feel we have a lot of catching up to do. What do you suggest?