Hello Houseseeker and thanks for your post.
As usual, Pacita was spot on with her answer. So long as you can qualify for a loan in only your name with just your income, then you may purchase the home by yourself. Depending on your wife's income and her current FICO scores, her past indebtedness may be more hindrance than help in obtaining a loan. Also, keep in mind that--even in a community property state--an inheritance is not considered community property so the funds from the inheritance belong solely to you, rather than to you and your wfie. Using the money for a home in your name only is wise since adding your wife's name to the home purchased with the inheritance will immediately make the property a communal asset.
To best protect yourself and your family member's bequest, talk with a qualified estate planning attorney for assistance. There are ways to keep assets purchased during a marriage separate and apart from the communal assets, but only a qualified attorney can provide you with a legal opinion of how this is done. And, this may be of benefit to you since Ginnie Mae (the guarantor of student loans) will eventually seek payment or garnishment to repay the student loans taken out by your wife. As Pacita noted, the title company will still require your wife to quit claim any ownership of the home you purchase in your name, as your "sole and separate" asset and this is done as part of the formal process of segregating assets.
Before you do anything, however, understand both your rights and obligations in using your inheritance for the purchase of a home and speak with an attorney to get the best and most accurate legal opinion of your options.
Grace Morioka, SRES, e-Pro
Area Pro Realty