First of all, congrats of having a great combined income. There is much you both can do from this point on to get started towards FI.
Your CC is costing you $125 a month just in interest. Or think of it this way, you can use your $7k in savings to pay off a big chunk, and the 15% you didn't pay in interest is like a 15% return on your money. I wouldn't keep your savings sitting around losing purchasing power. You couldn't invest it and guarantee a 15% return, so what to do with the savings and your CC is pretty clear IMO.
Regarding saving for a home, this is my very humble opinion...
I offer two solutions, the first being what I personally did. Pay off your CC as quickly as possible. Then, figure what is the minumum survival monthly expense amount you both need. Multiply this by 6 (at a minimum) and now you have a decent cushion. With this amount, you should never have to use your CC again unless your able to pay the balance off each month (with current income). However some argue CC's are good to have for emergencies, not the case...unless you can rack up rewards and pay the balance off the same month. I digress.
After savings, then start putting money away for a down payment on a house. Now you're probably thinking..."but we're ready to buy a house and don't want to rent anymore, and this seems like a very conservative approach." It is. Many people underestimate the cost of home ownership and I don't know you and I don't judge, but generally speaking those that carry balances on CC aren't financially prepared to take on home ownership. Even if it's 2-3 years more down the road for you, that's okay. Homes will always be there, but at least you'll have saved properly for it. You can always speed up the process by finding the cheapest living arrangements that you can tolerate to ramp up the savings.
The second solution would be to pay off your CC and then start saving for your home. However a $200K home with a 15 year mortgage is going to be half your net take home once you factor mortgage, PMI, taxes, maintenance (don't underestimate), utilities...so yes, you could probably get into a home. But I'm willing to bet it will be stressful. Ultimately because a 15 yr mortgage is agressive for the size of house and your income. Why not take out a 30 yr mortgage and pay it down as though it were 15? At least you have the option.
Remember, you're asking this question in a forum where the ultimate goal is FI as early as possible. This means spending less, saving more or making more. You won't be doing any of these by getting a house this early in your careers. That's my two cents.