First of all, if you are military, have you considered the possibility of Space A? It is truly the cheapest, but leave you with the possibility of not getting on the flight in either direction.
Our situation is a catch 22 when flying commercially. We fly from Naples, a much smaller airport. This creates an additional connection to the main part of the overall flight, causing additional cost. If we were to travel to Rome, we would save the airfare, but then the catch 22 is the additional cost of gas and parking (if driving), train fare and other transportation fees to get from train to airport (if traveling that way), wasted time, etc. We just pay to fly from Naples.
What we have found is just looking at Kayak for basic airline rates gives us an idea of what we will most likely be paying. We always start looking as soon as we have a definite date set for the vacation or whatever your reason for flying. The further out usually means cheapest fares.
Check the airline websites. For example, we find a price we are ok with on Kayak and check the official airline webite instead. The price was actually cheaper on the airline website than Kayak. In addition, the official website offered more schedule options that worked out better for the time of day we wanted to arrive. The cost was no more than what was advertised on kayak. I have found that Kayak tends to offer some lower rates, but many of the flights leave less than an hour layover between connections and some of those layovers can cause a normally 14-17 hour trip to be 33!
One other thing.......All airlines have partner airlines when flying across water. I prefer Lufthansa simply for the added room and comfort. They also partner with United, so you could (depending on where you are flying from and to) end up with United. I am not a fan of United. The seating is terribly cramped. However, for the same flight, you should check the pricing of United. The schedule may or may not be exactly the same. My example was that going through Lufthansa website, my TO America flight was the exact same on Lufthansa and United websites, but United had a later return flight, and the total cost ended up being cheaper too. Just something to think about.
I would be a bit afraid of purchasing separate tickets for different legs of the total flight. For example, you buy a ticket to London for cheaper overall fare (maybe). Unless you gave yourself a huge layover, say your first flight has mechanical problems and does not leave for a few hours, causing you to miss your next flight. What is the next airlines policy on missing a flight? In addition, separate tickets means you have to go to baggage pickup, then transfer it to the next airline. Wasted time and aggrivation. If you bought the entire flight through an airline, even if you have multiple connections, you only have to touch the luggage when you get in America to go through customs. The original airline always makes sure the luggage pushes through to the connecting flight, saving you from luggage retrieval. Missing a connection when buying entire flight through one ticket means less hassle to fix a mess created by delays.
Please stay away from Alitalia if they service one of your locations. They partner with Air France. Check the details. Alitalia is the worst and always has been.
Also, not sure about Germany, but Italy requires us to have a document stating we can remain in the country past the 3 month passport stamp. If your country has one of those documents, make sure you take it with you when you travel. I have found Germany to be the most strict with travel documents in the airport. They almost take a magnifying glass to ours and almost rejected my son's because he was 12 when we moved to Italy and 15 when we first flew commercially. His looks obviously had changed. They hesitated to let him through.
Oh, for us, $1,000 is about the cheapest we have found to get us to America.
Sorry for the long winded explaination. Hope it was not too confusing.