All right here goes.
I'd really have to know your joint income and expenses to make a full recommendation. I'll assume your only current debt is the $53,000 of student loans.
Step 1.
Student loan $13,500 (6.8%) - Pay this one down ASAP. Don't bother about extra repayments on the other loans until this one is cleared.
Step 2.
Cut back on a few expenses - cable, mobile phone, restaurants, hair care, and spending money would be my targets. You should be able to free up $300 extra a month, without a drastic change in lifestyle.
Step 3.
You can't afford that house (this is assuming your partner has the same income and similar expenses).
A good place to start
http://www.nytimes.com/interactive/business/buy-rent-calculator.htmlYou'll be fine in your current studio with a baby. Could easily get away with it until they're 2 years old. Your rent seems low enough and local house prices high enough that I'd stay where you are, focus on repaying that high interest debt, then investing or continuing to pay down the other debt.
If either of you have retirement plans that allow for employer match then I'd make sure you are contributing enough to get maximum match.
I'd only focus on home ownership if you can find a much better priced property, or if I've severely underestimated your partners income.
PS with a baby you won't have the time or energy to maintain a garden, or clean a whole house. So a studio really isn't a bad place to be,