How realistic is it that I will be able to get a home within the 250,000 range in the next year or so?
Very unlikely in the next year. The debt/income ratio isn't good enough, and your credit score needs to show at least a year of regular payments without late or default issues before you can start asking for mortgages in this range. You don't mention how long you've been employed at these incomes, this can also count against you if you haven't both been employed for a full year at these incomes. They will look even more unfavorably on the employment situation if they aren't both full time jobs, although if you have a full year's worth of paychecks showing the income is regular then that might mitigate the full time/part time issue.
next year or so?
If you pay down your high interest debt (car, credit cards), and maintain employment (keep your check stubs and tax returns, the loan officer will want copies), then there's a slight chance.
And, from this quick snap shot of our finances, does it look like we would be able to qualify for a USDA loan?
Probably not. Mostly for the same reasons - the only time a USDA loan helps is when you would be able to get a regular loan if you had the down payment.
Even with an available down payment of 50k, you wouldn't be able to get a regular loan, therefore it's unlikely that you'd qualify for a USDA loan.
If you are anxious to get into a house, choose something much smaller, in the 100k-150k range. It would improve your debt/loan ratio enough that you might then qualify for a USDA loan. However, I think you'd still have issues if you haven't both been employed at this rate of income for at least a year, and have made regular payments on all your debts for at least a year.
I'll echo what others have suggested, though, strengthen your credit, eliminate as much of your high interest debt as you can (car, credit cards), and keep your jobs for a year or two. Start a savings plan so you can contribute a small down payment - at least 3-5% of the desired home price - when you are in a better position to buy. During this time keep track of your paycheck stubs, you may need them to prove income over the time period your loan officer will request.
Note that even with a USDA loan you still have to pay closing costs, and those can run several thousand dollars, so don't expect to be able to come to the table with no cash.
Lastly, there's good reason to be very conservative regarding house cost and size. If you can, consider buying the house as if you only had the 46k per year. Move the debt to the person making the lower income, and if you buy the house in the name of the person only making 46k per year, then the debt/loan ratio looks very positive. Further it may be that the credit history of that person is better, and the employment history is better. If one of you has better history in these ways, then you might have a better chance if only one of you buys the house. Banks can't tell you about this, but it does work. Keep in mind, though, that if you two part ways it could be very unhappy since one would be left with all the debt and the house would be in the other's name. Not a great situation to be in, so make sure that you both carefully consider the risks associated with the decisions made.