1. If you are applying for the loan in both names, we work off of both incomes with the lower of the two borrower's middle credit score. Unless one of you has a score lower than minimum requirements, this will more likely come into play ona conventional mortgage which uses credit score to help determine Fannie Mae hits to rates. If you are going FHA, the credit score does not factor into determining rate.
2. If you end up with just your wife on the loan due to either credit scores, or you have too much debt with you on the loan with her, then the loan (debt) will be in her name but in MS you will be on the deed of trust at closing and have joint survivorship to the property should anything ever happen such as death or divorce.
3. As for the least down payment, there is bond money but it's not quite as attractive as the old bond money program as the bond money is an actual loan now. Secondly, there are income limits for the household that make exclude you from the program if you make too much household income. It varies by county. USDA rural housing is a popular form of financing now as it allows 100% financing but again there are income limits and the property has to be in certain geographic locations. If you are not a veteran, then VA wouldn't apply but if you are that is a great option. Lastly, if none of the above works for you, then you are looking at 3.5% down on an FHA loan. Rates on it are good...3.875% on a fixed 30 right now. The monthly pmi sux but it's the price you pay for the downpayment.
Let me know if I didn't answer all your questions.