Thank you for your question, and congratulations on your planned marriage!
The good news is that relations between Russia and Europe are not an issue in this matter. Your future husband, as an EU citizen married with a third-country national has a right to exercise his freedom of movement in the EU together with you.
Practically, this means that you may go to Germany and settle there together after having gotten married in the US, and you are entitled to an automatic long-term residence permit.
Please note the following important information:
1. Theoretically, a visa for such a case is not required, because you are entitled to enter Germany on your passport, together with him, and the Apostilled marriage certificate, and an authorized translation into German of this certificate. However, to avoid any problem at the border, you may apply at the German Embassy in Washington, D.C. (or the nearest German Consulate) for a visa for third-country family members of EU nationals, which will mean that nobody will ask you any questions when landing in Europe. This becomes practically essential if you plan on landing in some other EU country first (i.e. airport transfer). However, you are entitled to a visa, as long as you are not a criminal or a risk to EU security (in other words, the vast majority of cases are approved);
2. What I said above does not apply to Italy itself (or if your future husband is also an German citizen). Because of the way EU law works, this automatic right of residence of third-country family members does not apply in the country of citizenship of the EU national. Why? Because he would be considered not to be "exercising his right of free movement" and therefore EU legislation would not be applicable. The conditions of immigration could indeed be quite hard in that case (proof of income, of housing etc.), because national (Italian) law would apply, instead of EU law. However, once you have the long-term residence card from Germany, you can later go to Italy without a visa and without any settlement problems (because he would be "returning from the exercise of his right of free movement").
I hope that the extra information is useful and was not confusing, since I find it very important for your case.
I look forward to your rating which is essential to my activity.
Dr I L Vlad