Approval for a mortgage has little to do with marriage/single and a lot to do with income, debt-to-income ratio, cost of home, timely payment of other bills, and credit score.
The easiest start is getting your credit report and score from one of the big three (Experian, TransUnion, Equifax) credit reporting agencies to look over your credit history. You can look online for the FICO score meaning, but most agencies consider a FICO score above 725 as good.
Also, on the credit report...do you have bills that were past due by 30 days? 60 days? 90 days? Each one of those can affect your score. Additionally, the front page will tell you your overall debt-to-income ratio in percentile form.
Once you review your credit report, take it to YOUR financial institution and have an advisor look over it (usually a free service) and they can provide recommendations how to improve your score as well as whether you are a good candidate or not for a mortgage.
Hope this helps and good luck
Financial manager for US Navy