If we file bankruptcy and move out of the U.S., will we be denied a visa/citizenship because of the bankruptcy?

This question should be asked of someone who practices immigration law in the specific country that you are considering as every country has its own immigration policies and procedures. It wouldn't seem like it would be an issue, after all the filing for bankruptcy is not a criminal act, but only someone familiar with the laws of your desired destination country can advise you.

The only concern that immigration has with granting someone residence as to their debt situation is if they are "likely to become a public charge." Typically that means the person owes money to a public hospital or needs to receive some kind of public benefits to survive. If you are currently in the US on an immigrant visa, leaving the US for more than one year typically will terminate your visa. Someone may have signed an Affidavit of Support when you applied for your visa guaranteeing that you will not be a public charge. If your debt includes a hospital bill, your sponsor may have to pay that debt when you file bankruptcy.

That is not a bankruptcy question. You will have to research the visa and immigration laws of the country to which you wish to move.

Bankruptcy will not affect your ability to get a visa. Nor, should it affect gaining citizenship in another country, but you should check with that country's citizenship and immigration laws.