It is unlikely you could be approved for mortgage financing with that credit score at this time.
Sit down with a Local Mortgage Banker to review your and your fiance's Income, Assets, and Credit. This review will advise you what actions you need to take to improve your credit score, and an approximate timeline to do so.
First, settle any outstanding debt. If you owe money on collection accounts, charge-offs and/or judgments, make payment arrangements and get these accounts paid promptly.
Next, begin rebuilding your credit. If you have current accounts with good payment histories, or even some previous late-payment-blemishes, make sure you continue to pay those accounts on time. If you do not have any existing credit accounts then you'll need to establish several in order to create a viable credit history.
I have found that CONSUMER ACTION is an excellent resource for objective advice on all things credit related. You'll find free and sincere advice on everything from settling collection accounts to rebuilding credit to building credit from scratch on their website. http://consumer-action.org/
Beware of anyone offering to "repair" your credit! The Federal Trade Commission issued a stern warning last year that such offers are scams. Find more from the FTC HERE: http://www.ftc.gov/bcp/edu/pubs/consumer/credit/cre13.shtm
The best way to buy a home is to have a decent credit history combined with sufficient Income and Assets for a home purchase.
The best way to have a decent credit history is to settle negative outstanding obligations and pay all your bills on time for at least two years.
As for what's available to first time home buyers. There are several programs available to those who qualify. These programs may provide thousands of dollars to help you buy a home. Not all lenders offer these programs, so it's important to carefully select the right lender. I deal with many lenders who offer a large variety of home mortgage products. I am sure we can find the right fit for you. Feel free to give me a call so we can chat about your needs, wants & unique situation. Based on our conversation I should be able to point you to the lender who can best serve your needs. My cell# is 316-250-9960.
In terms of your score, it appear too low to qualify as is. In terms of your finace's score, it is great and she may qualify, but if she attempts to qualify alone, you cannot use combined income. And your joint savings can only be used if she is on the account or there are other gifting options that can be looked at.
Your best bet is to sit down with a local lender and have them pull credit scores, verify incomes, look at debt ratios, and give you both options separately or together based on the factual findings. Good Luck.